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LIPIcs, Volume 397
40th International Symposium on Distributed Computing (DISC 2026)
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Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Symposium on Distributed Computing (DISC)
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- published at: 2026-11-02
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-454-3
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Complete Volume
LIPIcs, Volume 397, DISC 2026, Complete Volume
Abstract
LIPIcs, Volume 397, DISC 2026, Complete Volume
Cite as
40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 1-1292, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@Proceedings{mosesjr._et_al:LIPIcs.DISC.2026,
title = {{LIPIcs, Volume 397, DISC 2026, Complete Volume}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {1--1292},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026},
URN = {urn:nbn:de:0030-drops-282816},
doi = {10.4230/LIPIcs.DISC.2026},
annote = {Keywords: LIPIcs, Volume 397, DISC 2026, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 0:i-0:xx, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{mosesjr._et_al:LIPIcs.DISC.2026.0,
author = {Moses Jr., William K. and Censor-Hillel, Keren},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {0:i--0:xx},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.0},
URN = {urn:nbn:de:0030-drops-282150},
doi = {10.4230/LIPIcs.DISC.2026.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Adaptive Snapshots Require Visible Reads
Abstract
Snapshots are widely used to record the state of a running execution. Snapshots have been extensively studied in the literature, with the goal of improving performance and extending functionality. In this work, we consider adaptive snapshots over a set of m components. Adaptive snapshots provide a Click() operation that logically creates a new snapshot and an Observe(i) operation that returns the state of component i at the most recent Click. Several constructions of adaptive snapshots have recently been proposed; interestingly, none of them employs invisible reads, even though invisible reads can improve performance, sometimes significantly. In this paper, we ask whether it is possible to build an adaptive snapshot with invisible reads. We show that, even when restricting the snapshot algorithm to the single-writer, single-scanner setting, under reasonable assumptions satisfied by all existing adaptive snapshot implementations, adaptive snapshots with invisible reads are not linearizable.
Cite as
Niv Sulimany, Tomer Cory, and Erez Petrank. Adaptive Snapshots Require Visible Reads. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 1:1-1:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{sulimany_et_al:LIPIcs.DISC.2026.1,
author = {Sulimany, Niv and Cory, Tomer and Petrank, Erez},
title = {{Adaptive Snapshots Require Visible Reads}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {1:1--1:24},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.1},
URN = {urn:nbn:de:0030-drops-281076},
doi = {10.4230/LIPIcs.DISC.2026.1},
annote = {Keywords: Snapshot, Shared memory, Linearization, Concurrency}
}
Document
FinWhale: An Optimally Resilient 2 Rounds Terminating DAG Protocol
Abstract
DAG-based Byzantine Fault Tolerant (BFT) protocols provide high-throughput consensus under partial synchrony, but existing DAG protocols still require at least three message delays to commit decisions. In contrast, fast-path BFT protocols can achieve optimal two-message-delay termination under favorable conditions, though they do not naturally extend to DAGs.
We present FinWhale, the first DAG-based BFT protocol with a two-message-delay fast path. FinWhale extends Mysticeti with a novel fast-path commit mechanism that safely coexists with the protocol’s original slow-path rules. To preserve safety across different local DAG views, we introduce new commit structures based on FP-evidence blocks, enabling validators to combine fast-path and slow-path reasoning consistently.
FinWhale operates in the partially synchronous model with n = 3f+2p-1 validators, matching the known lower bound for fast Byzantine consensus. The protocol tolerates up to f Byzantine faults and achieves fast termination whenever at most 1 ≤ ~p ≤ ~f validators fail during the fast path. Our results show that optimal-latency fast paths can be integrated into uncertified DAG consensus protocols.
Cite as
Razya Ladelsky and Roy Friedman. FinWhale: An Optimally Resilient 2 Rounds Terminating DAG Protocol. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 2:1-2:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{ladelsky_et_al:LIPIcs.DISC.2026.2,
author = {Ladelsky, Razya and Friedman, Roy},
title = {{FinWhale: An Optimally Resilient 2 Rounds Terminating DAG Protocol}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {2:1--2:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.2},
URN = {urn:nbn:de:0030-drops-281085},
doi = {10.4230/LIPIcs.DISC.2026.2},
annote = {Keywords: DAG protocols, Byzantine Atomic Broadcast, Consensus, Fast Termination}
}
Document
Self-Stabilizing Algorithms in the Uniform Port Model
Abstract
We introduce a distributed computational model referred to as the uniform port model. An algorithm operating in this model is defined by means of local automata associated with the ports (a.k.a. half-edges) of the input graph. The crux of the uniform port model is that a single constant-size finite automaton is hosted by every port of every graph, making the model truly uniform. Moreover, since the new model explicitly supports the assignment of (input and) output labels to the graph’s (half-)edges, it facilitates natural formulations of (half-)edge-labeling problems such as maximal matching and sinkless orientation, which are outside the expressivity scope of prior node-centric truly uniform distributed computational models.
The main technical contribution of this paper is the design of efficient (i.e., with poly-logarithmic runtime) self-stabilizing uniform port algorithms, operating on general graphs, for various fundamental local symmetry breaking problems, including maximal independent set, maximal matching, sinkless orientation, and maximal node/edge k-coloring. While efficient self-stabilizing algorithms for local symmetry breaking problems have been extensively studied in stronger computational models, our work is the first to demonstrate the existence of such algorithms in a truly uniform model.
Cite as
Liam Brinker, Yuval Emek, and Oren Louidor. Self-Stabilizing Algorithms in the Uniform Port Model. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 3:1-3:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{brinker_et_al:LIPIcs.DISC.2026.3,
author = {Brinker, Liam and Emek, Yuval and Louidor, Oren},
title = {{Self-Stabilizing Algorithms in the Uniform Port Model}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {3:1--3:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.3},
URN = {urn:nbn:de:0030-drops-281094},
doi = {10.4230/LIPIcs.DISC.2026.3},
annote = {Keywords: truly uniform algorithms, uniform port model, self-stabilization, local symmetry breaking}
}
Document
How to Walk a Dog in Parallel: On Parallel Computation of the Discrete Fréchet Distance
Abstract
The Fréchet distance (also known as the dog-leash distance) is a well-studied and prevalent distance measure for polygonal curves. In this paper we present parallel algorithms for computing the discrete Fréchet distance between two curves, in both the PRAM and MPC models.
For two polygonal curves of length n, we show that the distance between them can be computed in the PRAM model in O(log n/ σ) rounds and Õ(n^{2+σ}) total work for any 0 < σ < 1. In the sublinear MPC model with n^ρ space per machine, it can be computed in O(log n / ρ²) rounds and Õ(n^{2+ρ}) total space. For c-packed curves, we match our bounds to the sequential algorithms, showing that a (1+{ε})-approximation of the distance can be computed in the PRAM model in O(log{n}+1/σ³) rounds and Õ(n^{1+σ}) total work, and in the sublinear MPC model in O(1 /ρ³) rounds and Õ(n^{1+ρ}) total space, for any constant {ε} > 0. As part of our algorithms for c-packed curves, we also present parallel algorithms for computing curve simplifications, which may be of independent interest.
Cite as
Leonid Barenboim, Arnold Filtser, Omrit Filtser, and Orr Fischer. How to Walk a Dog in Parallel: On Parallel Computation of the Discrete Fréchet Distance. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{barenboim_et_al:LIPIcs.DISC.2026.4,
author = {Barenboim, Leonid and Filtser, Arnold and Filtser, Omrit and Fischer, Orr},
title = {{How to Walk a Dog in Parallel: On Parallel Computation of the Discrete Fr\'{e}chet Distance}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {4:1--4:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.4},
URN = {urn:nbn:de:0030-drops-281107},
doi = {10.4230/LIPIcs.DISC.2026.4},
annote = {Keywords: Fr\'{e}chet Distance, PRAM, MPC}
}
Document
Deterministic Edge Coloring with Few Colors in CONGEST
Abstract
As the main contribution of this work we present deterministic edge coloring algorithms in the CONGEST model. In particular, we present an algorithm that edge colors any n-node graph with maximum degree Δ with (1+ε)Δ+O(√{log n}) colors in Õ(log^{2.5} n+log² Δ log n) rounds. This brings the upper bound polynomially close to the lower bound of Ω(log n/log log n) rounds that also holds in the more powerful LOCAL model [Chang, He, Li, Pettie, Uitto; SODA'18]. As long as Δ ≥ c√{log n} our algorithm uses fewer than 2Δ-1 colors and to the best of our knowledge is the first polylogarithmic-round CONGEST algorithm achieving this for any range of Δ.
As a corollary we also improve the complexity of edge coloring with 2Δ-1 colors for all ranges of Δ to Õ(log^{2.5} n+log² Δ log n). This improves upon the previous O(log⁸ n)-round algorithm from [Fischer, Ghaffari, Kuhn; FOCS'17].
Our approach builds on a refined analysis and extension of the online edge-coloring algorithm of Blikstad, Svensson, Vintan, and Wajc [FOCS’25], and more broadly on new connections between online and distributed graph algorithms. We show that their algorithm exhibits very low locality and, if it can additionally have limited local access to future edges (as distributed algorithms can), it can be derandomized for smaller degrees. Under this additional power, we are able to bypass classical online lower bounds and translate the results to efficient distributed algorithms. This leads to our CONGEST algorithm for (1+ε)Δ+O(√{log n})-edge coloring. Since the modified online algorithm can be implemented more efficiently in the LOCAL model, we also obtain (marginally) improved complexity bounds in that model.
Cite as
Joakim Blikstad, Yannic Maus, and Tijn de Vos. Deterministic Edge Coloring with Few Colors in CONGEST. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{blikstad_et_al:LIPIcs.DISC.2026.5,
author = {Blikstad, Joakim and Maus, Yannic and de Vos, Tijn},
title = {{Deterministic Edge Coloring with Few Colors in CONGEST}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {5:1--5:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.5},
URN = {urn:nbn:de:0030-drops-281111},
doi = {10.4230/LIPIcs.DISC.2026.5},
annote = {Keywords: edge coloring, CONGEST, deterministic, online algorithms}
}
Document
Optimality and Trade-Offs in Fast BFT SMR
Abstract
Leader-based state-machine replication (SMR) protocols are the most popular and widely deployed protocols in practice. However, they suffer from high latency because all commands need to be routed through and ordered by the leader. Fast SMR protocols overcome this limitation by executing non-conflicting commands with minimal latency of two message delays (measured from the time the client sends its request). These protocols in the crash-fault setting have attracted significant interest in both academia and industry. This interest is driven by practical advantages over leader-based protocols, including lower latency for non-conflicting commands, higher throughput, greater availability, and increased fairness. While Fast SMR is well studied in the crash-fault setting, the Byzantine fault-tolerant (BFT) setting remains much less studied, with only a small number of existing Fast BFT SMR protocols. In this paper, we present tight upper and lower bounds on the replication factor required for Fast BFT SMR. We also present a suboptimal protocol that illustrates a trade-off between replication factor and recovery efficiency.
Cite as
Neil Giridharan, Minh Tung Nguyen, Ittai Abraham, Allen Clement, Natacha Crooks, and Pierre Sutra. Optimality and Trade-Offs in Fast BFT SMR. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 6:1-6:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{giridharan_et_al:LIPIcs.DISC.2026.6,
author = {Giridharan, Neil and Nguyen, Minh Tung and Abraham, Ittai and Clement, Allen and Crooks, Natacha and Sutra, Pierre},
title = {{Optimality and Trade-Offs in Fast BFT SMR}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {6:1--6:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.6},
URN = {urn:nbn:de:0030-drops-281122},
doi = {10.4230/LIPIcs.DISC.2026.6},
annote = {Keywords: Fast state machine replication, consensus, partial synchrony, fault-tolerance}
}
Document
Solvability of Approximate Agreement on Graphs and Simplicial Complexes
Abstract
Approximate agreement tasks on graphs are discrete relaxations of consensus, where each process in a distributed system is given as input a vertex on a graph G, and processes have to output vertices that lie on a clique of G contained in the convex hull of the input vertices. Although such tasks have been widely studied in a variety of models, graph classes and notions of convexity, it remains largely open for which classes of graphs these problems are solvable in asynchronous systems.
In this work, we give a complete topological characterisation of the t-resilient solvability of approximate agreement on graphs and simplicial complexes in asynchronous shared-memory systems with read-write registers. As a result, we answer several open problems related to different variants of approximate agreement on graphs. For example, we give the first proof of Ledent’s conjecture [PODC 2021] about the wait-free solvability of clique agreement.
In fact, we show a more general result: clique agreement is t-resilient solvable on a graph G if and only if its clique complex is (t-1)-connected in the homotopical sense. We also show that clique and monophonic agreement are solvable on the same class of graphs, but there exists a separation between monophonic and geodesic agreement, answering a question by Alistarh et al. [TCS 2023]. In the message-passing setting, our results imply new resilience bounds for asynchronous approximate agreement and round lower bounds for synchronous approximate agreement on graphs.
Cite as
Joel Rybicki and Yaroslav Verbitsky. Solvability of Approximate Agreement on Graphs and Simplicial Complexes. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{rybicki_et_al:LIPIcs.DISC.2026.7,
author = {Rybicki, Joel and Verbitsky, Yaroslav},
title = {{Solvability of Approximate Agreement on Graphs and Simplicial Complexes}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {7:1--7:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.7},
URN = {urn:nbn:de:0030-drops-281138},
doi = {10.4230/LIPIcs.DISC.2026.7},
annote = {Keywords: approximate agreement, impossibility results, algebraic topology}
}
Document
Predictions Can Only Help! Communication Efficient Byzantine Agreement with Predictions
Abstract
In Byzantine agreement with predictions each process begins with an input value and some (unreliable) prediction bits. Recently, it has been shown that with classification predictions - where the predictions predict each process to be honest or faulty - Byzantine agreement can be completed more quickly than without predictions, circumventing the traditional Ω(f) round lower bound. However, existing algorithms either handle limited prediction errors or send too many messages. Moreover, they all exchange Ω(n³) bits - enough to allow the processes to approximately agree on the classifications. In fact, it almost seemed necessary to share a significant number of prediction bits if one wanted to tolerate a high number of incorrect predictions.
In this paper, we show that this high level of communication is not inherent to a round-efficient protocol with predictions. We provide an unauthenticated algorithm with near-optimal 𝒪̃(n²) communication complexity and optimal resilience t < n/3. Furthermore, with authentication, we give an algorithm with optimal 𝒪(n²κ) communication complexity (where κ is a security parameter) and near-optimal resilience t < (1/2 - ε)n for any constant ε > 0. All of our results achieve optimal round complexity for any number of errors in the predictions.
Cite as
Marc Dufay, Muhammad Ayaz Dzulfikar, and Seth Gilbert. Predictions Can Only Help! Communication Efficient Byzantine Agreement with Predictions. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 8:1-8:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{dufay_et_al:LIPIcs.DISC.2026.8,
author = {Dufay, Marc and Dzulfikar, Muhammad Ayaz and Gilbert, Seth},
title = {{Predictions Can Only Help! Communication Efficient Byzantine Agreement with Predictions}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {8:1--8:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.8},
URN = {urn:nbn:de:0030-drops-281145},
doi = {10.4230/LIPIcs.DISC.2026.8},
annote = {Keywords: Byzantine agreement, Algorithm with predictions, Synchronous network}
}
Document
Quadratic Asynchronous DKG from Plain Setup
Abstract
Asynchronous distributed key generation (ADKG) is a fundamental primitive for building threshold cryptosystems and fault-tolerant distributed protocols in adversarial network settings. A central objective in this line of work is to achieve ADKG with O(n²) communication and constant round complexity under minimal setup assumptions. Recent progress has led to subcubic-communication ADKG protocols under different trade-offs. Feng and Tang (CRYPTO 2025) presented an ADKG protocol with O(n²) communication and O(1) rounds, but at the cost of a cubic-communication setup phase in which each party posts a linear-sized public key on a public bulletin board. In contrast, Abraham et al. (PODC 2026) achieved an ADKG protocol with a standard setup phase, where each party posts only a constant-sized public key, but with O(n^{2+1/k}) communication and O(k) rounds for a tunable parameter k ≤ log{n}. These results leave open whether one can simultaneously obtain constant-round complexity and quadratic communication under a standard setup phase.
In this work, we resolve this open problem by presenting the first ADKG protocol that achieves O(n²) communication and O(1) rounds while requiring only a standard setup phase in which each party posts a constant-sized public key on a public bulletin board. Our protocol is resilient to a strongly adaptive adversary corrupting up to f < n/3 parties and assumes only random oracles and secure erasures, both of which are also assumed by prior subcubic-communication ADKG constructions.
Cite as
Ittai Abraham, Renas Bacho, and Gilad Stern. Quadratic Asynchronous DKG from Plain Setup. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 9:1-9:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{abraham_et_al:LIPIcs.DISC.2026.9,
author = {Abraham, Ittai and Bacho, Renas and Stern, Gilad},
title = {{Quadratic Asynchronous DKG from Plain Setup}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {9:1--9:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.9},
URN = {urn:nbn:de:0030-drops-281153},
doi = {10.4230/LIPIcs.DISC.2026.9},
annote = {Keywords: Asynchronous Network, Consensus, Distributed Key Generation, Leader Election}
}
Document
It Does Not Matter How You Define Locally Checkable Labelings
Abstract
Locally checkable labeling problems (LCLs) form the foundation of the modern theory of distributed graph algorithms. First introduced in the seminal paper by Naor and Stockmeyer [STOC 1993], these are graph problems that can be described by listing a finite set of valid local neighborhoods. The definition strikes a careful balance between two objectives: the family of LCL problems is broad enough to capture numerous problems that are of interest to researchers working in this field, yet restrictive enough so that it is possible to prove strong theorems that hold for all LCL problems. In particular, the distributed complexity landscape of LCL problems is now very well understood.
Yet what we are seeing more and more often is that there are LCL problems with unexpected, counterintuitive properties: there are LCL problems that admit a distributed quantum advantage [SODA 2026] or benefit from shared randomness [ICALP 2025]; there is an LCL problem whose complexity in the LOCAL model depends on whether state transitions are restricted to computable functions [DISC 2026]; we can construct LCL problems with unnatural round complexities [STOC 2018]; and many questions related to the distributed complexity of LCL problems are undecidable [STOC 1993, PODC 2017]. Overall, the LCL problems seem to be a poor proxy for the family of natural local graph problems. With large volumes of research on LCL problems, the following questions are getting ever more pressing: Are we studying the right problem family? Maybe the above counterintuitive features are mere artifacts of the specific definition of LCLs introduced by Naor and Stockmeyer, and they disappear if we slightly restrict the family of LCL problems?
In this work we show that the family of LCL problems is extremely robust to variations. We present a very restricted family of locally checkable problems (essentially, the "node-edge checkable" formalism familiar from round elimination, restricted to regular unlabeled graphs); most importantly, such problems cannot directly refer to e.g. the existence of short cycles. We show that one can translate between the two formalisms with little overhead; in particular, all counterintuitive properties listed above hold also for restricted LCLs.
Cite as
Antonio Cruciani, Avinandan Das, Alesya Raevskaya, and Jukka Suomela. It Does Not Matter How You Define Locally Checkable Labelings. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 10:1-10:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{cruciani_et_al:LIPIcs.DISC.2026.10,
author = {Cruciani, Antonio and Das, Avinandan and Raevskaya, Alesya and Suomela, Jukka},
title = {{It Does Not Matter How You Define Locally Checkable Labelings}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {10:1--10:24},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.10},
URN = {urn:nbn:de:0030-drops-281166},
doi = {10.4230/LIPIcs.DISC.2026.10},
annote = {Keywords: Locally checkable labeling problems, Distributed graph algorithms}
}
Document
Lifeline: Optimal Validated Byzantine Agreement Under Minimal Synchrony
Abstract
The synchronous model allows solutions to (variants of) Byzantine Agreement (BA) to be deterministic and achieve the asymptotically optimal O(n) rounds and O(n²) bits of communication where n is the number of parties. In this paper, we study deterministic protocols for the validated BA problem in a model in which every communication link is either synchronous or partially synchronous. Our main result is that in the region of an honest majority, feasibility implies optimality: For every f < n/2, the minimal network conditions required for validated BA to be solvable against f byzantine faults, are also sufficient for it to be solvable optimally, i.e., with O(f) rounds and O(f²) communication. In particular, validated BA against minority byzantine faults can be solved when the synchronous links in the network form a mere path (f synchronous links) as efficiently (up to constant factors) as when all communication links are synchronous (Ω(f²) synchronous links).
Cite as
Yuval Efron and Ling Ren. Lifeline: Optimal Validated Byzantine Agreement Under Minimal Synchrony. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 11:1-11:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{efron_et_al:LIPIcs.DISC.2026.11,
author = {Efron, Yuval and Ren, Ling},
title = {{Lifeline: Optimal Validated Byzantine Agreement Under Minimal Synchrony}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {11:1--11:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.11},
URN = {urn:nbn:de:0030-drops-281171},
doi = {10.4230/LIPIcs.DISC.2026.11},
annote = {Keywords: Byzantine agreement, granular synchrony, optimal communication complexity}
}
Document
Efficient Randomized LL/SC That Preserves History Independence
Abstract
We study the fundamental problem of implementing m linearizable LL/SC objects with constant expected step complexity in a system of n processes, using bounded base objects commonly available in hardware. Assuming that each process may have at most τ outstanding LL() operations, the best known deterministic algorithm requires Ω(n²τ + m) base objects (CAS objects and registers) [Guy E. Blelloch and Yuanhao Wei, 2020]. Previously, no comparable randomized algorithm was known.
By employing randomization and FADD objects in addition to CAS objects, we obtain a space bound of O(nτ+m) against the weak adaptive adversary. For m = O(1) this matches a lower bound for algorithms using CAS objects and registers [Zahra Aghazadeh and Philipp Woelfel, 2015].
In addition, our object can be employed by quiescently history-independent (QHI) algorithms: Whenever no operation on the object is pending and no process has an outstanding LL() operation, its internal memory state is uniquely determined by the values of the m LL/SC objects. An important application is a recent QHI dynamic hashing algorithm, which uses Θ(m) hardware LL/SC objects to maintain a hash table of size m [Hagit Attiya et al., 2025]. But LL/SC is not available in hardware, and prior to our work no wait-free or efficient lock-free software implementation of LL/SC with similar properties was known. Our work demonstrates that one can actually implement the hashing algorithm on available hardware, without an asymptotic increase in step and space complexity, under the reasonable assumption that m = Ω(n).
Cite as
Dante Bencivenga, Homa Habashi, and Philipp Woelfel. Efficient Randomized LL/SC That Preserves History Independence. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 12:1-12:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{bencivenga_et_al:LIPIcs.DISC.2026.12,
author = {Bencivenga, Dante and Habashi, Homa and Woelfel, Philipp},
title = {{Efficient Randomized LL/SC That Preserves History Independence}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {12:1--12:24},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.12},
URN = {urn:nbn:de:0030-drops-281180},
doi = {10.4230/LIPIcs.DISC.2026.12},
annote = {Keywords: LL/SC, concurrent algorithms, history independence, randomized algorithms, wait-freedom}
}
Document
Tight Energy Lower Bounds for Distributed Graph Algorithms
Abstract
There has been a significant recent interest in designing distributed algorithms in the SLEEPING model that minimize the energy (a.k.a awake) complexity, which measures the number of rounds a node is awake during the algorithm. A node spends non-trivial resources (messages, energy, etc.) only when it is awake and not while sleeping. Energy complexity has been studied for various fundamental problems with respect to minimizing the maximum (worst-case) or the average number of rounds a node is awake.
It has been shown that the energy complexities of several fundamental problems such as leader election (LE), broadcast, Minimum Spanning Tree (MST), Maximal Independent Set (MIS) is exponentially smaller compared to their respective best-possible round complexities in the standard CONGEST model (where nodes can only send messages of small size). This raises a fundamental question of whether such significant energy gains are possible for many other fundamental problems.
Our main contribution is a general and powerful technique for showing energy lower bounds using information theory. It gives almost a "plug-in" way to show energy lower bounds for various problems in the standard CONGEST model. Our information-theoretic technique allows us to leverage known lower bounds on communication complexity to obtain new, almost optimal (up to logarithmic factors) polynomial (in n) lower bounds on energy complexity - for both worst-case and average-case - for fundamental graph problems such as triangle enumeration, All-Pairs Shortest Paths (APSP), diameter computation, minimum weight cycle, Maximum Independent Set (MaxIS), Minimum Dominating Set (MinDS), Minimum Vertex Cover (MinVC). The energy lower bounds of these problems match their respective round lower bounds, implying that one cannot obtain any significant gains in energy complexity.
Cite as
Fabien Dufoulon, Gopal Pandurangan, and Peter Robinson. Tight Energy Lower Bounds for Distributed Graph Algorithms. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 13:1-13:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{dufoulon_et_al:LIPIcs.DISC.2026.13,
author = {Dufoulon, Fabien and Pandurangan, Gopal and Robinson, Peter},
title = {{Tight Energy Lower Bounds for Distributed Graph Algorithms}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {13:1--13:24},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.13},
URN = {urn:nbn:de:0030-drops-281198},
doi = {10.4230/LIPIcs.DISC.2026.13},
annote = {Keywords: distributed graph algorithm, energy complexity, information-theoretic lower bound}
}
Document
Is a LOCAL Algorithm Computable?
Abstract
Common definitions of the "standard" LOCAL model tend to be sloppy and even self-contradictory on one point: do the nodes update their state using an arbitrary function or a computable function? So far, this distinction has been safe to neglect, since problems where it matters seem contrived and quite different from e.g. typical local graph problems studied in this context.
We show that this question matters even for locally checkable labeling problems (LCLs), perhaps the most widely studied family of problems in the context of the LOCAL model. Furthermore, we show that assumptions about computability are directly connected to another aspect already recognized as highly relevant: whether we have any knowledge of n, the size of the graph. Concretely, we show that there is an LCL problem Π with the following properties:
1) Π can be solved in 𝒪(log n) rounds if the LOCAL model is uncomputable.
2) Π can be solved in 𝒪(log n) rounds in the computable model if we know any upper bound on n.
3) Π requires Ω(√n) rounds in the computable model if we do not know anything about n. We also show that the connection between computability and knowledge of n holds in general: for any LCL problem Π, if you have any bound on n, then Π has the same round complexity in the computable and uncomputable models.
Cite as
Antonio Cruciani, Avinandan Das, Massimo Equi, Henrik Lievonen, Diep Luong-Le, Augusto Modanese, and Jukka Suomela. Is a LOCAL Algorithm Computable?. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{cruciani_et_al:LIPIcs.DISC.2026.14,
author = {Cruciani, Antonio and Das, Avinandan and Equi, Massimo and Lievonen, Henrik and Luong-Le, Diep and Modanese, Augusto and Suomela, Jukka},
title = {{Is a LOCAL Algorithm Computable?}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {14:1--14:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.14},
URN = {urn:nbn:de:0030-drops-281201},
doi = {10.4230/LIPIcs.DISC.2026.14},
annote = {Keywords: Locally checkable labeling problems, LOCAL model}
}
Document
Near-Optimal Distributed 2-Ruling Sets on Graphs with Low Arboricity
Abstract
Given a graph G = (V,E), a β-ruling set is a subset of nodes S ⊆ V that is independent, and each node in V is at distance at most β from some node in S. In this paper, we present almost optimal distributed algorithms for finding 2-ruling sets in the classical LOCAL model. Our main contribution is a randomized algorithm that w.h.p. computes a 2-ruling set on any n-node graph with bounded arboricity in O(log log n) rounds. In fact, the algorithm works up to arboricity O(log log n), improves exponentially over the prior state of the art that can be achieved by combining [Barenboim, Elkin, Pettie, Schneider; JACM'16], [Ghaffari; SODA'16], and [Bisht, Kothapalli and Pemmaraju; PODC'14], and nearly matches the lower bound of Ω(log log n / log log log n) [Balliu, Brandt, Kuhn, Olivetti; FOCS'20]. The domination parameter β = 2 is optimal for algorithms with runtime log^{o(1)}n: on graphs with arboricity 2, there is a lower bound of Ω(√{log n}) rounds for MIS (i.e., β = 1) [Khoury, Schild; FOCS'25].
Additionally, we obtain improved algorithms for larger arboricity. For general graphs with arboricity α, we present a randomized algorithm that computes a 2-ruling set in Õ(log^{5/8} α +log^{5/3} log n) rounds. This improves exponentially over the state of the art for a large range of non-constant arboricity.
Our techniques extend beyond distributed computing. We present an O(log log log n)-round algorithm in the low-space Massively Parallel Computation (MPC) model that w.h.p. computes a 2-ruling set on any graph with arboricity up to 2^poly(log log n), improving exponentially over the state of the art from [Kothapalli, Pai, Pemmaraju; FSTTCS'20] combined with [Fischer, Giliberti, Grunau; SPAA'23].
Cite as
Malte Baumecker, Rustam Latypov, Yannic Maus, and Jara Uitto. Near-Optimal Distributed 2-Ruling Sets on Graphs with Low Arboricity. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 15:1-15:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{baumecker_et_al:LIPIcs.DISC.2026.15,
author = {Baumecker, Malte and Latypov, Rustam and Maus, Yannic and Uitto, Jara},
title = {{Near-Optimal Distributed 2-Ruling Sets on Graphs with Low Arboricity}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {15:1--15:25},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.15},
URN = {urn:nbn:de:0030-drops-281213},
doi = {10.4230/LIPIcs.DISC.2026.15},
annote = {Keywords: 2-ruling set, LOCAL model, CONGEST model, MPC model}
}
Document
eAID: Elastic Asynchronous Information Dispersal with Post-Dissemination Pruning
Abstract
Spreading and storing erasure-coded data effectively in distributed systems is challenging in practical settings. Consider a system of N nodes designed to tolerate up to F < N/2 failures. The dissemination of erasure-coded information is typically designed to complete only after receiving messages from N nodes, thereby preparing for the worst-case, but rare, scenario of F failures. In steady state, the remaining F nodes may in fact be healthy, but their resources are not counted. This leads to over-provisioning of storage for encoded data.
This paper introduces eAID, a novel elastic information dispersal algorithm that addresses this conundrum through a two-stage approach.
First, the core protocol estimates the actual number f of faulty nodes, rather than assuming the worst-case bound F. Dissemination completes quickly when messages are received from (N-f) nodes, and more gradually when fewer nodes respond. This flexibility enables the system to tune storage efficiency against latency. Second, after initial dissemination completes, eAID continues monitoring for additional responses. As responses arrive from up to N nodes, the system prunes the information stored at responding nodes accordingly.
A key technique enabling this seamless elasticity is an agile encoding scheme that varies the number of disseminated fragments while keeping both fragment size and the recovery threshold (F+1) fixed. Not only does this enable varying the number of disseminated fragments on the fly, it also allows nodes to discard encoded fragments autonomously. Crucially, this is achieved without maintaining complex metadata, without requiring nodes to reconstruct or re-encode information, and without global coordination for storage decisions.
We demonstrate the practicality of eAID by integrating it with a replicated key-value store and evaluating it in network environments with unpredictable latencies. The results show that eAID improves overall performance while significantly reducing long-term storage consumption.
Cite as
Rithwik Kerur, Divyakant Agrawal, Dahlia Malkhi, Michael K. Reiter, and Amit Wieder. eAID: Elastic Asynchronous Information Dispersal with Post-Dissemination Pruning. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 16:1-16:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{kerur_et_al:LIPIcs.DISC.2026.16,
author = {Kerur, Rithwik and Agrawal, Divyakant and Malkhi, Dahlia and Reiter, Michael K. and Wieder, Amit},
title = {{eAID: Elastic Asynchronous Information Dispersal with Post-Dissemination Pruning}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {16:1--16:25},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.16},
URN = {urn:nbn:de:0030-drops-281227},
doi = {10.4230/LIPIcs.DISC.2026.16},
annote = {Keywords: Fault Tolerance, Erasure Coding, Information Dispersal, Consensus}
}
Document
Efficient Stable Population Protocols for Parity and Beyond
Abstract
The population protocol model studies pairwise interactions among simple, indistinguishable agents, each storing a single state from a fixed space. In the probabilistic variant, a random scheduler selects an interacting pair uniformly at random at each step. Besides state utilisation, we consider stabilisation time, defined as the number of interactions until a final configuration, divided by the population size n. A protocol is time-efficient if it stabilises in polylogarithmic time, space-efficient if it uses polylogarithmic number of states, stable if it converges to the correct answer with probability 1, and silent if no states change after stabilisation.
We present a systematic methodology that enables the design of protocols that are efficient, stable and silent for computing congruence predicates. We first address the parity problem, where agents compute the parity of a designated sub‑population size, and then generalise the approach to congruence modulo an arbitrary integer m. While prior work focused on problem‑specific designs, our approach provides a systematic framework for efficient multi‑stage protocols. Central to this approach is the weight system, an efficient counting mechanism based on the novel concept of population weights (or simply weights), combined with majority computation and operating via implicit conversion between unary and binary representations. The weight system is integrated within the proposed modular MC+ computing paradigm, which leverages extensive prior work on clocking mechanisms, efficient anomaly signalling, and a switching mechanism that guarantees fallback to a slow yet always‑correct stable protocol. The new approach yields the first efficient parity and congruence protocols using O(log³ n) states and achieving silent stabilisation in O(log³ n) time, providing significant progress towards the research directions identified by Czerner et al. (2024). We also discuss the impact of the implicit conversion on other problems, including the computation and alternative representation of (sub-)population sizes, a postulate raised by Doty and Eftekhari (2021).
All algorithmic solutions presented in this paper guarantee silent stabilisation in time both expected and with high probability (whp) defined as 1-n^{-η}, for any fixed constant η > 0.
Cite as
Leszek Gąsieniec, Tytus Grodzicki, Tomasz Jurdziński, Jakub Kowalski, and Grzegorz Stachowiak. Efficient Stable Population Protocols for Parity and Beyond. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 17:1-17:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{gasieniec_et_al:LIPIcs.DISC.2026.17,
author = {G\k{a}sieniec, Leszek and Grodzicki, Tytus and Jurdzi\'{n}ski, Tomasz and Kowalski, Jakub and Stachowiak, Grzegorz},
title = {{Efficient Stable Population Protocols for Parity and Beyond}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {17:1--17:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.17},
URN = {urn:nbn:de:0030-drops-281239},
doi = {10.4230/LIPIcs.DISC.2026.17},
annote = {Keywords: Population protocols, MC+ protocols, parity, congruence}
}
Document
Consensus with Stochastic Broadcast
Abstract
We study binary consensus in the stochastic broadcast model, which assumes n ≥ 2 processes communicating synchronously by message broadcasts. At each round, every process broadcasts a message to all the other processes. Each broadcast succeeds independently with some probability p, where p ∈ [0,1] is a parameter of the model. If a broadcast succeeds, all processes receive the message, and if it fails, no process receives the message. The sender does not know whether its broadcast was successful or not. In this model, consensus is not solvable; the objective is to design, for a given number of rounds r, consensus algorithms that terminate in r rounds, minimizing the probability of error (disagreement). This problem has been studied in depth for 2 processes [DISC 2025]. We extend the study to n > 2.
We identify two key algorithms in the 1-round setting. In Algorithm pref1, each process decides 1 unless it knows of no input 1. In Algorithm courteous, each process decides the more frequent value in its view, and, in case of a tie, the process decides the negation of its own input value. It turns out that for small values of p courteous is better, while for larger values, pref1 is better.
Our main results are lower bounds. For n = 3 processes and one round, we show that courteous is optimal for p ∈ [0,2/3], and pref1 is optimal for p ∈ [2/3,1]. To obtain this result, we develop a specialized theory that extends the combinatorial topology approach to a probabilistic setting.
For an arbitrary (but fixed) number n > 3 of processes, we show that among all 1-round consensus algorithms, courteous is optimal for p ∈ [0,1/n], and that pref1 is asymptotically optimal for p → 1.
For multi-round algorithms, we show that (unlike the case of n = 2 processes) repeating r times an optimal 1-round algorithm is not optimal for n ≥ 3 processes. Nevertheless, we present a 2-round algorithm, called sweep, that guarantees the best error probability for the number of transmissions. Specifically, for every number n of processes, repeating sweep r times entails at most rn broadcasts, and results in error probability q^{rn}, where q = 1-p is the probability that a broadcast fails.
We believe that our results provide another step towards the goal of a general topological theory of randomized distributed computing.
Cite as
Pierre Fraigniaud, Boaz Patt-Shamir, and Sergio Rajsbaum. Consensus with Stochastic Broadcast. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{fraigniaud_et_al:LIPIcs.DISC.2026.18,
author = {Fraigniaud, Pierre and Patt-Shamir, Boaz and Rajsbaum, Sergio},
title = {{Consensus with Stochastic Broadcast}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {18:1--18:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.18},
URN = {urn:nbn:de:0030-drops-281244},
doi = {10.4230/LIPIcs.DISC.2026.18},
annote = {Keywords: stochastic communication, distributed agreement, distributed consensus, Kripke graph, topology of distributed algorithms}
}
Document
Õptimal Distributed Maximum Flow Approximation in Undirected Planar Graphs
Abstract
Persistent efforts in recent years have been devoted to devising distributed algorithms for fundamental optimization problems in planar graphs. In particular, for Single-Source Shortest-Paths, there is an Õ(D²)-rounds exact algorithm [Li, Parter STOC'19] for directed planar graphs, and an Õ(D)-rounds (1+o(1))-approximation algorithm [Rozhon, Grunau, Haeupler, Zuzic, Li STOC'22] for undirected planar graphs (where D is the graph’s hop-diameter). Recently [Abd-Elhaleem, Dory, Parter, Weimann PODC'25], a matching bound for the exact case was obtained for the Maximum st-Flow problem. Namely, an Õ(D²)-rounds exact algorithm for directed planar graphs. However, for the approximate case, they give a D⋅ n^o(1)-rounds (1-o(1))-approximation algorithm for undirected planar graphs that works only for the special case where both s and t lie on the same face.
In this paper, we remove the restriction that both s and t must lie on the same face (we also eliminate the n^o(1) factor). Namely, we present the first distributed near-optimal Õ(D)-rounds (1-o(1))-approximation algorithm for Maximum st-Flow in general undirected planar graphs. Our main technical contribution is a distributed implementation of the classical Reif’s [SICOMP'83] centralized algorithm. This is achieved by a careful recursive incision procedure on the planar dual G^* of the graph G. It is challenging, because we need to simulate dynamic changes (incisions) over the dual graph G^*, while we can only communicate over the input graph G.
Cite as
Yaseen Abd-Elhaleem, Michal Dory, and Oren Weimann. Õptimal Distributed Maximum Flow Approximation in Undirected Planar Graphs. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{abdelhaleem_et_al:LIPIcs.DISC.2026.19,
author = {Abd-Elhaleem, Yaseen and Dory, Michal and Weimann, Oren},
title = {{Õptimal Distributed Maximum Flow Approximation in Undirected Planar Graphs}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {19:1--19:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.19},
URN = {urn:nbn:de:0030-drops-281251},
doi = {10.4230/LIPIcs.DISC.2026.19},
annote = {Keywords: Maximum flow, minimum st-cut, shortest paths, planar graphs, distributed computing}
}
Document
A Lock-Free Move-To-Front List with a Working Set Bound
Abstract
We give a lock-free move-to-front list that stores a set of keys, organized so that more recently accessed keys are closer to the front of the list. The amortized step complexity of an Insert, Delete or Search operation on a key k is proportional to the size of the operation’s working set - the number of distinct keys accessed since the last operation on k - plus the operation’s point contention. No previous concurrent, linearizable dynamic set has a complexity bound that adapts to the access pattern of keys. The number of reachable list nodes is at most the number of keys in the set plus contention.
Cite as
Shalom Asbell and Eric Ruppert. A Lock-Free Move-To-Front List with a Working Set Bound. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{asbell_et_al:LIPIcs.DISC.2026.20,
author = {Asbell, Shalom and Ruppert, Eric},
title = {{A Lock-Free Move-To-Front List with a Working Set Bound}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {20:1--20:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.20},
URN = {urn:nbn:de:0030-drops-281263},
doi = {10.4230/LIPIcs.DISC.2026.20},
annote = {Keywords: lock-free, move-to-front, self-adjusting data structures, working set bound, amortized analysis, linearizability}
}
Document
Randomized Tree-Intersection Leader Election
Abstract
We present a randomized leader election algorithm for synchronous complete n-node graphs in the CONGEST model that introduces a highly tunable trade-off between time complexity and the per-node message complexity. By adjusting a single branching parameter, 𝓁, system designers can smoothly shift the algorithmic burden from execution time to per-node message complexity, all while maintaining a strictly sublinear total message complexity of O(√n log^{1.5} n). We achieve this by utilizing dynamically truncated 𝓁-ary tree expansions coupled with a novel "silent pulse" verification mechanism. By forcing the expansions to form exact-volume almost-complete trees, nodes can safely aggregate topological weights without overshooting the sublinear message bounds. Specifically, our algorithm achieves O(log_𝓁 √{n log n}) time (round) complexity and O(𝓁) per-node message complexity. This flexibility allows networks with tight bandwidth constraints to operate with a minimal O(1) per-node burden, while high-bandwidth environments can collapse the election into O(1) time units.
Cite as
Yuval Emek, Shay Kutten, Ido Rafael, and Gadi Taubenfeld. Randomized Tree-Intersection Leader Election. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 21:1-21:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{emek_et_al:LIPIcs.DISC.2026.21,
author = {Emek, Yuval and Kutten, Shay and Rafael, Ido and Taubenfeld, Gadi},
title = {{Randomized Tree-Intersection Leader Election}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {21:1--21:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.21},
URN = {urn:nbn:de:0030-drops-281277},
doi = {10.4230/LIPIcs.DISC.2026.21},
annote = {Keywords: Leader election, randomized algorithms, sublinear communication, per-node message complexity, CONGEST model}
}
Document
The Local Complexity of Certifying Parity
Abstract
In this paper, we consider the problem of locally certifying that the size of a network is even, or more generally, congruent to some fixed number. The parity property is one of the simplest global properties, and it plays an intriguing role in local certification. On the one hand, it is one of the simplest properties in cycles because it is equivalent to 2-colorability, and hence can be certified with a single bit. On the other hand, in general graphs, no non-trivial lower bound on the size of the certificates is known, and the known upper bound basically consists in certifying the exact value of n. In addition, the nature of the problem makes all the known lower bound approaches fail.
We uncover a surprising landscape for parity across different models and graph structures:
- In general graphs equipped with identifiers, when allowing verification radius 2, parity can be certified with a constant number of bits.
- But in the model of anonymous graphs and allowing verification radius only 1, parity requires Ω(log log^*n) bits.
- Finally, in bounded expansion graph classes (such as bounded-degree graphs and planar graphs), the lower bound does not apply: in the same restricted model we can design a constant-size certification.
We introduce several new tools that we expect to be useful in other contexts, in particular ways to encode a parent at each node with a constant number of bits (via implicit use of the IDs and conflict-free colorings) and a new lower bound technique, with complex topologies and higher-order Ramsey-type arguments.
Cite as
Nicolas Bousquet, Laurent Feuilloley, Jorge Valenzuela, and Sébastien Zeitoun. The Local Complexity of Certifying Parity. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{bousquet_et_al:LIPIcs.DISC.2026.22,
author = {Bousquet, Nicolas and Feuilloley, Laurent and Valenzuela, Jorge and Zeitoun, S\'{e}bastien},
title = {{The Local Complexity of Certifying Parity}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {22:1--22:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.22},
URN = {urn:nbn:de:0030-drops-281285},
doi = {10.4230/LIPIcs.DISC.2026.22},
annote = {Keywords: Local certification, proof-labeling schemes, locally checkable proofs, space complexity, parity, congruence, lower bound}
}
Document
Fairness in the Wild: Secure Atomic Swap with External Incentives
Abstract
Atomic swaps enable asset exchanges across blockchains without relying on trusted intermediaries, and are a key component of decentralized finance (DeFi) ecosystems. Recently, Rapidash (Financial Cryptography 2025) introduced an atomic swap protocol that remains incentive compatible under user-miner collusion, by ensuring that the honest strategy forms a coalition-resistant Nash equilibrium. However, Rapidash’s model assumes a closed system where players act solely based on internal protocol incentives. In practice, parties may be influenced by external incentives such as off-chain rewards or adversarial bribes, which can undermine such equilibrium guarantees.
In this work, we introduce a new game-theoretic notion, bounded maximin fairness, which ensures that honest participants remain protected against rational adversaries with arbitrary but bounded external incentives. We construct an atomic swap protocol that satisfies this notion, while preserving the equilibrium properties of prior work in the absence of external influence. As we show, our protocol is easy to implement and can be instantiated even in Bitcoin’s limited scripting language.
Cite as
Hao Chung, Elaine Shi, Sri AravindaKrishnan Thyagarajan, and Elisaweta Masserova. Fairness in the Wild: Secure Atomic Swap with External Incentives. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 23:1-23:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{chung_et_al:LIPIcs.DISC.2026.23,
author = {Chung, Hao and Shi, Elaine and Thyagarajan, Sri AravindaKrishnan and Masserova, Elisaweta},
title = {{Fairness in the Wild: Secure Atomic Swap with External Incentives}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {23:1--23:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.23},
URN = {urn:nbn:de:0030-drops-281292},
doi = {10.4230/LIPIcs.DISC.2026.23},
annote = {Keywords: Fair exchange, mechanism design, game-theoretic approaches to distributed computing, blockchains}
}
Document
Designing Local Distributed Mechanisms
Abstract
Mechanism design studies algorithms as games with the goal of designing algorithms that incentivise participants to be truthful: to behave according to their real preferences. In this work we introduce a new notion: local distributed mechanisms. These are truthful mechanisms that have an implementation as fast distributed algorithms and have non-trivial approximation guarantees. We show how monotone distributed optimisation algorithms can be automatically transformed into truthful mechanisms using the seminal result known as Myerson’s Lemma. We demonstrate mechanisms for four fundamental graph problems: maximum-weight independent set, minimum-weight vertex cover, minimum-weight dominating set, and a variant of weighted colouring.
We study distributed mechanism design in two settings. In the trusted setting we are only interested in a distributed implementation of a mechanism and assume that the algorithm is executed correctly. We also study what happens when the strategic agents themselves are responsible for running the algorithm, and show that a large class of algorithms cannot be implemented. Despite this impossibility, we are able to design a non-trivial incentive-compatible mechanism for weighted independent set problem.
Our work extends previous work in Distributed Algorithmic Mechanism Design (DAMD) in a new direction. Instead of studying global problems like routing or leader election, we study local resource allocation problems. Our algorithms are simple and thus potentially practical. Local algorithms are particularly interesting for highly dynamic large-scale systems, and there are many potential future application domains, e.g. demand-side load management in electric grids or resource allocation in IoT computing.
Cite as
Juho Hirvonen and Sara Ranjbaran. Designing Local Distributed Mechanisms. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 24:1-24:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{hirvonen_et_al:LIPIcs.DISC.2026.24,
author = {Hirvonen, Juho and Ranjbaran, Sara},
title = {{Designing Local Distributed Mechanisms}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {24:1--24:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.24},
URN = {urn:nbn:de:0030-drops-281305},
doi = {10.4230/LIPIcs.DISC.2026.24},
annote = {Keywords: local algorithms, game theory, algorithmic mechanism design}
}
Document
Fast Deterministic Distributed Degree Splitting
Abstract
We obtain faster distributed algorithms for the directed and undirected degree splitting problems. In the directed degree splitting problem the goal is to orient the edges of a graph to minimize the discrepancy between in-degree and out-degree at every vertex. In the undirected degree splitting problem the goal is to color the edges red and blue to minimize the discrepancy between red-degree and blue-degree at every vertex.
In particular, we design a deterministic Local algorithm of complexity 𝒪(ε^{-1} ⋅ log n) for computing a directed degree split with discrepancy at most ε ⋅ deg(v) for every vertex v ∈ V. The dependence on n in our runtime is optimal due to the Ω(log n) lower bound by Chang, Kopelowitz and Pettie (STOC 2016), which already holds for ε = 1/3. We improve upon the previous result by Ghaffari, Hirvonen, Kuhn, Maus, Suomela and Uitto (DISC 2017) by eliminating all additional dependence on ε beyond the leading ε^{-1} factor. Furthermore, we extend our algorithm to compute undirected degree splits with the same discrepancy guarantee and in the same asymptotic runtime. Beyond our deterministic Local results, we also provide faster randomized algorithms for the same problems.
A key ingredient in our approach is a connection to the hypergraph sinkless orientation (HSO) problem introduced by Brandt, Maus, Narayanan, Schager and Uitto (SODA 2025). We extend their randomized HSO algorithm to apply to a larger class of instances, which in turn reduces the runtime of our randomized degree splitting algorithms. We also provide deterministic and randomized CONGEST algorithms for solving HSO.
Degree splittings are a natural tool to solve other graph problems via a recursive divide-and-conquer strategy. As a demonstration of this claim, we apply our degree splitting algorithm to show that (3/2 + ε)Δ-edge coloring can now be solved in 𝒪(ε^{-1} ⋅ log²Δ ⋅ log n + ε^{-2} ⋅ log n) rounds in Local. For constant ε and Δ = 𝒪(2^{log^{1/3} n}), this runtime matches the current state-of-the-art for (2Δ-1)-edge coloring in Ghaffari and Kuhn (FOCS 2021).
Cite as
Yannic Maus, Alexandre Nolin, and Florian Schager. Fast Deterministic Distributed Degree Splitting. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 25:1-25:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{maus_et_al:LIPIcs.DISC.2026.25,
author = {Maus, Yannic and Nolin, Alexandre and Schager, Florian},
title = {{Fast Deterministic Distributed Degree Splitting}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {25:1--25:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.25},
URN = {urn:nbn:de:0030-drops-281315},
doi = {10.4230/LIPIcs.DISC.2026.25},
annote = {Keywords: LOCAL model, degree splitting}
}
Document
Space-Efficient Lock-Free Linear-Probing Hash Table
Abstract
Linear probing is one of the simplest and most space-efficient approaches to hash table design, and is widely used in sequential settings due to its compact memory layout. However, designing a concurrent linear-probing hash table with strong liveness guarantees has proved difficult, and only a handful of such algorithms have been proposed, all of which either restrict concurrency or rely on large per-entry metadata, thereby compromising space efficiency.
We present a lock-free linear-probing hash table with wait-free lookups that retains the core advantages of sequential linear probing while handling contention gracefully. Our design uses only a small amount of metadata per table entry: a constant number of additional bits when using LL/SC, or a logarithmic number of bits when using CAS. The algorithm is linearizable and lock-free, supports insert, delete, and wait-free lookup operations, and is able to safely reclaim space used by deleted elements without rebuilding the table.
We analyze the amortized step complexity of our hash table assuming no concurrent insertions of the same key, and show that each operation has expected amortized step complexity matching that of sequential linear probing, up to the point contention per key.
Cite as
Hagit Attiya, Rotem Oshman, and Noa Schiller. Space-Efficient Lock-Free Linear-Probing Hash Table. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 26:1-26:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{attiya_et_al:LIPIcs.DISC.2026.26,
author = {Attiya, Hagit and Oshman, Rotem and Schiller, Noa},
title = {{Space-Efficient Lock-Free Linear-Probing Hash Table}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {26:1--26:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.26},
URN = {urn:nbn:de:0030-drops-281321},
doi = {10.4230/LIPIcs.DISC.2026.26},
annote = {Keywords: linear probing, LL/SC, CAS, tombstones}
}
Document
Adaptive Self-Organization in Anonymous Dynamic Networks
Abstract
We introduce the problem of adaptive self-organization in which the nodes of an anonymous, synchronous dynamic network must distributively change the collective distribution of their responses (or "colors") as a function of time-varying environmental signals, even when these signals are only perceived locally and the network topology changes adversarially. Specifically, a signal adversary may change the type of signal and which node(s) witness that signal arbitrarily between rounds. If a signal (or lack thereof) s persists in the system for sufficiently long, the dynamic network must stabilize such that nodes' colors closely approximate r(s), a goal distribution defined by the problem instance. By symmetry, deterministic nodes can only hope to solve homogeneous instances of adaptive self-organization, i.e., those in which all nodes stabilize with the same color. We present a linear-time, logarithmic-memory, deterministic algorithm for this class of instances that works even when the multiplicity and location of signal witnesses change arbitrarily. We then give a randomized extension of this algorithm that solves arbitrary (i.e., not necessarily homogeneous) instances of adaptive self-organization with high probability in the same time and space bounds.
Cite as
Garrett Parzych and Joshua J. Daymude. Adaptive Self-Organization in Anonymous Dynamic Networks. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 27:1-27:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{parzych_et_al:LIPIcs.DISC.2026.27,
author = {Parzych, Garrett and Daymude, Joshua J.},
title = {{Adaptive Self-Organization in Anonymous Dynamic Networks}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {27:1--27:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.27},
URN = {urn:nbn:de:0030-drops-281330},
doi = {10.4230/LIPIcs.DISC.2026.27},
annote = {Keywords: Dynamic networks, anonymous nodes, broadcast, self-organization, biological distributed algorithms}
}
Document
Generalizing LCL Complexity Gaps to Unbounded Degree via Monadic Second-Order Properties
Abstract
The last decade of research on the LOCAL model has seen tremendous progress in understanding locally checkable labeling (LCL) problems, culminating in an almost complete classification of the possible complexities LCL problems can exhibit. In particular, on undirected trees, Chang and Pettie showed that there is no LCL problem with complexity between ω(log n) and n^o(1) [Yi-Jun Chang and Seth Pettie, 2017] and Chang showed that, for every positive integer k, there is no LCL problem with complexity between ω(n^{1/(k+1)}) and o(n^{1/k}) [Yi-Jun Chang, 2020]; additionally, which side of each gap a problem is found on is decidable.
While the class of LCL problems - which, roughly speaking, consists of problems for which the correctness of a solution can be described by a finite set of allowed node configurations, which in turn can be locally verified by a constant-time algorithm - includes many important problems, it has one major restriction: problems can be defined only on bounded degree graphs, which consequently restricts all the classification and gap results mentioned above.
In this work, we propose a generalization of LCL problems to unbounded degree using Presburger monadic second-order (PMSO) formulas; more specifically, we consider what we call Local PMSO (LPMSO) problems, i.e., problems whose correct solutions are both finitely described by a PMSO formula and locally verifiable by a LOCAL algorithm in constant time - this class contains many of the important problems studied in the LOCAL model but defines them on unbounded degree graphs. As our main result we prove that, on unbounded degree rooted trees, the aforementioned ω(log n)-n^{o(1)} and ω(n^{1/(k+1)})-o(n^{1/k}) complexity gaps (and their decidability) extend to the class of LPMSO problems.
We obtain our gap results by proving two theorems that may be of independent interest:
1) We show that computing just a solution of an LPMSO problem is asymptotically as hard as computing both a solution and a certificate for its correctness, if the certification is based on the minimal automaton verifying the PMSO formula.
2) By modifying the minimal verification automaton slightly, we create a so-called rational multiset tree automaton whose run on the input rooted tree encodes both a solution and a certificate for its correctness; then we show that computing a run of any rational multiset tree automaton on a rooted tree is asymptotically equivalent to solving the same problem on a rooted tree whose degree is bound by a constant depending only on the problem description.
Cite as
Chiara Piombi. Generalizing LCL Complexity Gaps to Unbounded Degree via Monadic Second-Order Properties. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 28:1-28:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{piombi:LIPIcs.DISC.2026.28,
author = {Piombi, Chiara},
title = {{Generalizing LCL Complexity Gaps to Unbounded Degree via Monadic Second-Order Properties}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {28:1--28:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.28},
URN = {urn:nbn:de:0030-drops-281343},
doi = {10.4230/LIPIcs.DISC.2026.28},
annote = {Keywords: Distributed graph algorithms, LOCAL model, locally checkable labeling problems, Presburger monadic second-order logic, rooted trees, complexity gaps}
}
Document
Triangle-Free Coloring in LOCAL via Resilient Lovász Local Lemma
Abstract
The Lovász Local Lemma (LLL) is a probabilistic tool that has been shown to be of central importance in the study of distributed algorithms. For example, the constructive LLL is known to be complete for the class of locally-checkable labeling problems with o(log n) randomized complexities in the LOCAL model. One classic application of the LLL is in coloring graphs with some sparse structure, such as triangle-free graphs. Triangle-free coloring therefore serves as a benchmark problem for techniques for sublogarithmic randomized distributed algorithms.
The state-of-the-art distributed triangle-free coloring algorithm of Pettie and Su [ICALP 2013, Information and Computation 2015] uses Δ/k colors (where k can be up to (1/4 - ε)ln Δ) and consists of O(k+log^* n) applications of the distributed LLL. However, the distributed LLL is itself a difficult problem; despite significant study, the fastest algorithms known require O(log_Δ n) or O(Δ/logΔ) + log^O(1)log n rounds, and no log^o(1) n-round algorithms exist except for restrictive special cases or graph classes such as trees. These LLL applications therefore dominate the round complexity of the algorithm.
In this work, we adapt the Pettie-Su’s algorithm so that the resulting LLL instances can be solved in log^O(1) log n rounds, by employing the "resilience" definition of Davies [SODA 2023]. This gives an O(k)+log^O(1) log n complexity (since the LLL is not needed when k = log^ω(1) log n), essentially causing the LLL steps to no longer be the bottleneck of the algorithm. As a corollary we obtain the first log^O(1) log n-round algorithms for coloring triangle-free graphs with o(Δ) colors. The same framework also yields a companion girth-5 algorithm, using (1+ε)Δ/ln Δ colors in O(k)+ log^O(1) log n rounds, matching the best known existential upper bound for the number of colors.
The LLL instances we use are among the most difficult for which efficient LOCAL algorithms have been shown, and we hope that this sheds further light on the solvability of the distributed LLL and may lead to further efficient applications.
Cite as
Peter Davies-Peck and Xusheng Zhang. Triangle-Free Coloring in LOCAL via Resilient Lovász Local Lemma. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 29:1-29:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{daviespeck_et_al:LIPIcs.DISC.2026.29,
author = {Davies-Peck, Peter and Zhang, Xusheng},
title = {{Triangle-Free Coloring in LOCAL via Resilient Lov\'{a}sz Local Lemma}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {29:1--29:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.29},
URN = {urn:nbn:de:0030-drops-281358},
doi = {10.4230/LIPIcs.DISC.2026.29},
annote = {Keywords: Distributed Graph Coloring, Triangle-free Graphs, Lov\'{a}sz Local Lemma}
}
Document
Near-Optimal Population Protocols on Bounded-Degree Trees
Abstract
We investigate space-time trade-offs for population protocols in sparse interaction graphs. In complete interaction graphs, optimal space-time trade-offs are known for the leader election and exact majority problems. However, it has remained open whether other graph families exhibit similar space-time complexity trade-offs, as existing lower bound techniques do not extend beyond highly dense graphs.
In this work, we show that - unlike in complete graphs - population protocols on bounded-degree trees do not exhibit significant asymptotic space-time trade-offs for leader election and exact majority. For these problems, we give constant-space protocols that have near-optimal worst-case expected stabilisation time. These new protocols achieve a linear speed-up compared to the state-of-the-art.
Our results are based on two novel protocols, which we believe are of independent interest. First, we give a new fast self-stabilising 2-hop colouring protocol for general interaction graphs, whose stabilisation time we bound using a stochastic drift argument. Second, we give a self-stabilising tree orientation algorithm that builds a rooted tree in optimal time on any tree. As a consequence, we can use simple constant-state protocols designed for directed trees to solve leader election and exact majority fast. For example, we show that "directed" annihilation dynamics solve exact majority in O(n² log n) steps on directed trees.
Cite as
Joel Rybicki, Jakob Solnerzik, and Robin Vacus. Near-Optimal Population Protocols on Bounded-Degree Trees. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{rybicki_et_al:LIPIcs.DISC.2026.30,
author = {Rybicki, Joel and Solnerzik, Jakob and Vacus, Robin},
title = {{Near-Optimal Population Protocols on Bounded-Degree Trees}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {30:1--30:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.30},
URN = {urn:nbn:de:0030-drops-281369},
doi = {10.4230/LIPIcs.DISC.2026.30},
annote = {Keywords: population protocols, distributed graph algorithms}
}
Document
Non-Leaking Concurrent Objects
Abstract
Abstract specifications of concurrent objects determine which values operations may return, but they also implicitly constrain which information operations may know, for example the arguments of other operations that do not affect their outcome, or even whether such operations occurred. Concrete implementations, while correct with respect to the abstract specification, may nonetheless expose additional information through their internal coordination mechanisms.
We introduce a framework for reasoning about information leakage in concurrent implementations. The framework uses epistemic logic to compare what a process may know under an abstract specification with what it may know in a concrete implementation, using the abstract object itself as the reference for permissible observations. This yields several notions of non-leaking implementations.
Using this framework, we investigate both the possibilities and limitations of non-leaking implementations. We present fully-non-leaking wait-free implementations of multi-valued registers and bounded max registers, but show that a fully-non-leaking unbounded max register cannot be implemented in a wait-free manner from finite-state base objects. We then consider a weaker guarantee, obtaining argument-non-leaking implementations of stacks, queues, and approximate agreement. These results demonstrate that non-leakage guarantees are often compatible with correctness and progress requirements, while also indicating their limitations.
Cite as
Hagit Attiya, Rotem Oshman, Noa Schiller, and Corentin Travers. Non-Leaking Concurrent Objects. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 31:1-31:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{attiya_et_al:LIPIcs.DISC.2026.31,
author = {Attiya, Hagit and Oshman, Rotem and Schiller, Noa and Travers, Corentin},
title = {{Non-Leaking Concurrent Objects}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {31:1--31:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.31},
URN = {urn:nbn:de:0030-drops-281372},
doi = {10.4230/LIPIcs.DISC.2026.31},
annote = {Keywords: non-leaking implementations, epistemic logic, knowledge, concurrent objects, decision tasks}
}
Document
Wait-Free Replicated Data Types and Fair Reconciliation
Abstract
Replication ensures data availability in fault-prone distributed systems. The celebrated CAP theorem stipulates that replicas cannot guarantee both strong consistency and availability under network partitions. A popular alternative, adopted by CRDTs, is to relax consistency to be eventual. It enables progress to be wait-free, as replicas can serve requests immediately, based on their local states.
Yet, wait-free replication faces a key challenge: due to asynchrony and concurrency, operations may be constantly reordered, leading to results inconsistent with their original contexts and preventing them from stabilizing over time. Moreover, a particular client may experience starvation when, from some point on, each of its operations is reordered at least once. This may lead to pathological scenarios, when the locally observed effect of each of the client’s operation is later rejected by the system.
We make two contributions. First, we formalize the problem addressed by wait-free replicated data types (e.g., CRDTs) as eventual state-machine replication. We then augment it with stability and fairness ensuring, respectively, that (1) all replicas share a growing stable prefix of operations, and (2) no client starves. Second, we present a generic DAG-based framework to achieve eventual state-machine replication for any replicated data type, where replicas exchange their local views and merge them using a reconciliation function. We then propose reconciliation functions ensuring stability and fairness.
Cite as
Petr Kuznetsov, Maxence Perion, and Sara Tucci-Piergiovanni. Wait-Free Replicated Data Types and Fair Reconciliation. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 32:1-32:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{kuznetsov_et_al:LIPIcs.DISC.2026.32,
author = {Kuznetsov, Petr and Perion, Maxence and Tucci-Piergiovanni, Sara},
title = {{Wait-Free Replicated Data Types and Fair Reconciliation}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {32:1--32:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.32},
URN = {urn:nbn:de:0030-drops-281380},
doi = {10.4230/LIPIcs.DISC.2026.32},
annote = {Keywords: Replication, Revocation, Eventual consistency, CAP, CRDT, DAGs, Fairness}
}
Document
Distributed Triangle and Simplex Enumeration in Hypergraphs
Abstract
In the last decade, subgraph detection and enumeration have emerged as central problems in distributed graph algorithms. This is largely due to the problems' theoretical challenges and practical applications. In this paper, we initiate the systematic study of distributed sub-hypergraph enumeration in hypergraphs. To this end, we (1) introduce several computational models for hypergraphs that generalize the CONGEST model for graphs and evaluate their relative computational power, (2) devise algorithms for distributed triangle and simplex enumeration in our computational models and prove their optimality in two such models by showing matching lower bounds, (3) introduce classes of sparse and "everywhere sparse" hypergraphs and describe efficient distributed algorithms for triangle and simplex enumeration in these classes, and (4) describe general techniques that we believe to be useful for designing efficient algorithms in our hypergraph models.
Cite as
Duncan Adamson, Will Rosenbaum, and Paul G. Spirakis. Distributed Triangle and Simplex Enumeration in Hypergraphs. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 33:1-33:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{adamson_et_al:LIPIcs.DISC.2026.33,
author = {Adamson, Duncan and Rosenbaum, Will and Spirakis, Paul G.},
title = {{Distributed Triangle and Simplex Enumeration in Hypergraphs}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {33:1--33:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.33},
URN = {urn:nbn:de:0030-drops-281396},
doi = {10.4230/LIPIcs.DISC.2026.33},
annote = {Keywords: Triangle Enumeration, Simplex Enumeration, Hypergraph, Distributed Algorithms, CONGEST}
}
Document
Counting in Population Protocols on Graphs
Abstract
We consider the problem of counting the number of agents in a population protocol where the agents are connected by an underlying graph G = (V,E) with |V| = n nodes. In each step, a random scheduler selects an edge uniformly at random, and the incident nodes make a state transition. As per standard assumptions, agents are identical and anonymous, that is, have no identifiers. To break symmetry, in each interaction one of the agents is declared as the initiator uniformly at random. Our size counting protocol uses Õ(n) states and stabilizes in O(𝐁(G)⋅log²(n) + 𝐋(G)⋅log(n)) interactions with high probability, where 𝐁(G) is the broadcast time and 𝐋(G) is the load balancing time. Our protocol is based on novel protocols for sampling independent random bits (given that the scheduler determines an initiator and responder) and approximating log n up to an additive error of O(log log n) with high probability. The latter uses O(polylog(n)) states and O(𝐁(G)⋅log² n) interactions. Both results may be of independent interest. The main protocol for exact counting requires the presence of a unique leader, the other two do not. None of the protocols requires any knowledge about the graph G. We conclude with impossibility results for terminating uniform population protocols that compute graph-size properties (like counting nodes or determining parity) with and without a leader.
Cite as
Petra Berenbrink, Robert Elsässer, Tom Friedetzky, Thorsten Götte, Lukas Hintze, and Dominik Kaaser. Counting in Population Protocols on Graphs. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 34:1-34:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{berenbrink_et_al:LIPIcs.DISC.2026.34,
author = {Berenbrink, Petra and Els\"{a}sser, Robert and Friedetzky, Tom and G\"{o}tte, Thorsten and Hintze, Lukas and Kaaser, Dominik},
title = {{Counting in Population Protocols on Graphs}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {34:1--34:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.34},
URN = {urn:nbn:de:0030-drops-281409},
doi = {10.4230/LIPIcs.DISC.2026.34},
annote = {Keywords: Population Protocols on Graphs, Counting, Load Balancing}
}
Document
General Convex Agreement with Near-Optimal Communication
Abstract
Byzantine Agreement (BA) considers a setting of n parties out of which up to t can be byzantine (malicious), and requires the honest parties to agree on a value subject to a condition called validity: if all honest parties have input v, the output agreed upon must be v. Convex Agreement (CA) strengthens BA by requiring the output agreed upon to lie in the convex hull of the honest parties' inputs. This validity condition captures aggregation tasks, such as robust learning and sensor fusion, where honest inputs may differ but should still constrain the final decision. Existing protocols for CA over general convexity spaces require at least Ω(L⋅n²) bits of communication for L-bit inputs, leaving a gap with BA’s Ω(L⋅n) lower bound.
We investigate this gap, and we present deterministic synchronous CA protocols with near-optimal communication complexity in the long-message regime. When L = Ω(n⋅κ), where κ is a security parameter, our protocols use 𝒪(L⋅nlog n) bits of communication for finite convexity spaces and 𝒪(L⋅n^{1+o(1)}) communication for Euclidean spaces ℝ^d. Our protocols also have asymptotically optimal round complexity 𝒪(n). If an upper bound L on the honest inputs' length in bits is known in advance, we achieve near-optimal resilience t < n/(ω+ε) for any constant ε > 0, where ω is the Helly number of the convexity space. When no such bound is known, we achieve resilience t < n/(ω+ε+1). Our main technical contribution is the use of extractor graphs to obtain a deterministic assignment of parties to committees, which is robust against adaptive adversaries.
As an application, our protocols can be used to obtain efficient solutions for parallel BA instances.
Cite as
Marc Dufay, Diana Ghinea, and Anton Paramonov. General Convex Agreement with Near-Optimal Communication. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 35:1-35:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{dufay_et_al:LIPIcs.DISC.2026.35,
author = {Dufay, Marc and Ghinea, Diana and Paramonov, Anton},
title = {{General Convex Agreement with Near-Optimal Communication}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {35:1--35:25},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.35},
URN = {urn:nbn:de:0030-drops-281417},
doi = {10.4230/LIPIcs.DISC.2026.35},
annote = {Keywords: byzantine agreement, convex agreement, communication complexity, long messages, extractors}
}
Document
Consensus Time in 3-Majority and 2-Choices Is Determined by the Maximum Initial Opinion Density
Abstract
We establish the correct parameter governing the convergence time of the 3-Majority and 2-Choices dynamics on the complete graph in the synchronous model. Recent work [Shimizu and Shiraga, PODC'25] provides matching upper and lower bounds on the number of rounds to consensus, but only in a weak sense: the bounds are shown to coincide for some initial opinion configuration.
In contrast, we obtain tight bounds in a strong sense, with upper and lower bounds matching up to logarithmic factors for every initial configuration. Let α^(0) be the initial opinion-frequency vector, and denote by ‖α^(0)‖_∞ its maximum entry. We show that 3-Majority reaches consensus in Θ̃(min{‖α^(0)‖_∞^{-1},√n}) rounds w.h.p., while 2-Choices reaches consensus in Θ̃(‖α^(0)‖_∞^{-1}) rounds w.h.p.
Our results demonstrate that the convergence time of both dynamics is governed not by aggregate statistics such as the number of opinions k or the squared 𝓁₂ norm of the initial opinion distribution, but rather by the extremal statistic ‖α^(0)‖_∞, the maximum initial opinion density.
Cite as
Niccolò D'Archivio. Consensus Time in 3-Majority and 2-Choices Is Determined by the Maximum Initial Opinion Density. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 36:1-36:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{darchivio:LIPIcs.DISC.2026.36,
author = {D'Archivio, Niccol\`{o}},
title = {{Consensus Time in 3-Majority and 2-Choices Is Determined by the Maximum Initial Opinion Density}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {36:1--36:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.36},
URN = {urn:nbn:de:0030-drops-281426},
doi = {10.4230/LIPIcs.DISC.2026.36},
annote = {Keywords: 3-Majority dynamics, 2-Choices dynamics, opinion dynamics, consensus, distributed algorithms, convergence time, infinity norm}
}
Document
LCLs Beyond Bounded Degrees
Abstract
The study of Locally Checkable Labelings (LCLs) has led to a remarkably precise characterization of the distributed time complexities that can occur on bounded-degree trees [Alkida Balliu et al., 2021; Balliu et al., 2019; Christoph Grunau et al., 2022; Yi-Jun Chang, 2020; Yi-Jun Chang et al., 2019; Yi-Jun Chang and Seth Pettie, 2019]. A central feature of this complexity landscape is the existence of strong gap results, which rule out large ranges of intermediate complexities. While it was initially hoped that these gaps might extend to more general graph classes [Yi-Jun Chang, 2020], this has turned out not to be the case [Balliu et al., 2018]. In this work, we investigate a different direction: we remain in the class of trees, but allow arbitrarily large degrees.
We focus on the polynomial regime, i.e. complexities of the form Θ(n^{1/k}) for k ∈ ℕ, and show that whether polynomial gap results persist in the unbounded-degree setting crucially depends on how LCLs are generalized beyond bounded degrees.
A complex construction in [Bousquet et al., 2025] shows that the polynomial gaps also vanish for LCLs on unbounded-degree trees. Rather than stopping at this negative result, we give a much simpler set of problems that already contradicts the existence of any polynomial gaps. The insight obtained from this cleaner construction is that for gap results to exist, we cannot allow problem definitions to distinguish infinitely many local cases.
This guides us to a natural class of problems for which polynomial gap results can still be recovered. We introduce Locally Finite Labelings (LFLs), which formalize the intuition that every node must fall into one of finitely many local cases, even in the presence of unbounded degrees.
Our main result shows that this restriction is sufficient to restore the polynomial gaps: for any LFL Π on trees of unbounded degrees, the deterministic LOCAL complexity of Π is either
- Θ(n^{1/k}) for some integer k ≥ 1, or
- O(log n).
Cite as
Gustav Schmid. LCLs Beyond Bounded Degrees. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 37:1-37:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{schmid:LIPIcs.DISC.2026.37,
author = {Schmid, Gustav},
title = {{LCLs Beyond Bounded Degrees}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {37:1--37:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.37},
URN = {urn:nbn:de:0030-drops-281431},
doi = {10.4230/LIPIcs.DISC.2026.37},
annote = {Keywords: Distributed graph algorithms, locally checkable labelings, LOCAL model, unbounded-degree trees, complexity gaps}
}
Document
Fast and Robust Information Spreading in the Noisy PULL Model
Abstract
Efficient information spreading in stochastic multi agent systems is a core challenge when communication is noisy, bandwidth limited, and agents lack global coordination. Yet biological systems, including ant colonies and fish schools, routinely overcome these constraints. A small number of informed individuals can reliably guide large, uncoordinated populations using minimal, noisy signals. Motivated by these observations, we study how reliable information dissemination can be achieved in such bio inspired settings.
A population of n agents, each with a binary preference, includes a designated subset of source agents, and the goal is to converge to the majority preference among the sources. In the noisy PULL(h) model, each agent observes noisy messages from h randomly sampled peers in every round. Prior work shows that convergence requires Ω(n/h) rounds even under favorable conditions. We ask how far we can push simplicity, with no synchronization at the start time and minimal message size, without compromising convergence speed.
We present a quasi self-stabilizing protocol using only 2-bit messages that converges from arbitrary initial states despite severe noise and initial asynchrony. It achieves optimal convergence time O((n/h)log n) with high probability, and in particular O(log n) time in the snapshot regime h = Θ(n). A key subroutine is an even simpler 1-bit protocol assuming simultaneous start, based on a natural two phase listen then amplify mechanism.
Together, our results show that simple, biologically inspired protocols can achieve optimal and robust information dissemination even in highly unreliable and uncoordinated systems.
Cite as
Niccolò D'Archivio, Amos Korman, Emanuele Natale, and Robin Vacus. Fast and Robust Information Spreading in the Noisy PULL Model. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 38:1-38:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{darchivio_et_al:LIPIcs.DISC.2026.38,
author = {D'Archivio, Niccol\`{o} and Korman, Amos and Natale, Emanuele and Vacus, Robin},
title = {{Fast and Robust Information Spreading in the Noisy PULL Model}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {38:1--38:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.38},
URN = {urn:nbn:de:0030-drops-281441},
doi = {10.4230/LIPIcs.DISC.2026.38},
annote = {Keywords: Information Spreading, Noisy Communication, Zealot Consensus, Self-Stabilization, Cooperative Transport, Crazy Ants, Natural Algorithms}
}
Document
Subcubic Coin Tossing in Asynchrony Without PKI
Abstract
We consider an asynchronous network of n parties, up to t of which are byzantine. We study common coin tossing, a task where the parties try to agree on an unpredictable random value, with some chance of failure due to the byzantine parties' influence. Coin tossing is a well-known and often-studied task due to its use in byzantine agreement.
We present a committee-based method to transform strong (rarely failing) binary common coins into weaker ones which asymptotically require less communication. For any k > 2 and ε > 0, we can transform a strong binary coin that costs Õ(n^k) bits of communication into a weak binary coin that costs Õ(ε^{-2k} n^{3 - 2/k}) bits. This latter coin tolerates ε n fewer byzantine parties than the strong coin it is based on, and it fails with an arbitrarily small constant probability.
With our method, we obtain a secure-channel-based perfectly secure common coin for t ≤ (1/4 - ε)n faults that costs Õ(n^{2.5}) bits, as well as a common coin based on cryptographic hashing for t ≤ (1/3 - ε)n faults that costs Õ(n^{7/3}κ) bits. These are to our knowledge the first PKI-free asynchronous common coins that cost o(n³) bits but nevertheless succeed with at least constant probability against t = Θ(n) (strongly) adaptive byzantine faults.
Cite as
Mose Mizrahi and Roger Wattenhofer. Subcubic Coin Tossing in Asynchrony Without PKI. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 39:1-39:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{mizrahi_et_al:LIPIcs.DISC.2026.39,
author = {Mizrahi, Mose and Wattenhofer, Roger},
title = {{Subcubic Coin Tossing in Asynchrony Without PKI}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {39:1--39:24},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.39},
URN = {urn:nbn:de:0030-drops-281455},
doi = {10.4230/LIPIcs.DISC.2026.39},
annote = {Keywords: Byzantine Agreement, Common Coin, Leader Election, Adaptive Adversary}
}
Document
What Can Be Computed in Average Anonymous Networks?
Abstract
We study deterministic distributed algorithms on random input graphs. We show that an extremely weak anonymous model of distributed computing can efficiently simulate the standard LOCAL and broadcast CONGEST models with high probability on random input graphs. In this weak model, all nodes are anonymous, and in each communication round, nodes broadcast a message to all their neighbors, receive an unordered set of messages from their neighbors, and update their local state. This is the SB model introduced by Hella et al. [PODC 2012], which is strictly weaker than the standard port-numbering PN model.
Specifically, we give a one-round deterministic SB-algorithm using O(log n)-bit messages that computes unique O(log n)-bit identifiers with high probability on anonymous networks sampled from G(n,p), where n^{ε-1} ≤ p ≤ 1/2 and ε > 0 is an arbitrarily small constant. Inspired by canonical labeling techniques in graph isomorphism testing, this construction allows existing distributed algorithms designed for the broadcast CONGEST and LOCAL models to be simulated in anonymous networks with only a small overhead. As a further application of our "anonymization" approach, we give a new algorithm for finding a triangle in O(1/ε) rounds on G(n,p) for p as above.
We also investigate the computational power of natural analogs of "Monte Carlo" and "Las Vegas" distributed graph algorithms in the random graph setting, and establish collapse and hierarchy results for both types of algorithms.
Cite as
Joel Rybicki, Oleg Verbitsky, and Maksim Zhukovskii. What Can Be Computed in Average Anonymous Networks?. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 40:1-40:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{rybicki_et_al:LIPIcs.DISC.2026.40,
author = {Rybicki, Joel and Verbitsky, Oleg and Zhukovskii, Maksim},
title = {{What Can Be Computed in Average Anonymous Networks?}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {40:1--40:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.40},
URN = {urn:nbn:de:0030-drops-281465},
doi = {10.4230/LIPIcs.DISC.2026.40},
annote = {Keywords: Average-case complexity, anonymous networks, unique identifiers, triangle finding, random graphs, color refinement}
}
Document
Strong Efficiency Lower Bounds for Byzantine Agreement
Abstract
Understanding the complexity of Byzantine agreement (BA) is a fundamental problem in distributed computing and cryptography. Existing round- or communication lower bounds either restrict the class of protocols they apply to in terms of communication, setup assumptions, or determinism. Another class of lower bounds holds only with respect to a very powerful (arguably unrealistic) adaptive adversary that can delete undelivered messages sent by a newly corrupted party while it was still honest. On the other hand, many popular BA protocols including the consensus protocol underlying the Algorand cryptocurrency assume only a standard adaptive adversary which cannot perform after-the-fact message removals. In this work, we aim to further narrow the gap between existing upper and lower bounds. We first show that unauthenticated BA has Ω(t²) messages complexity under an adaptive adversary even assuming randomization. This removes the restriction to multicast-based protocols in Abraham et al PODC'19. We then consider the restricted model of Dolev-Reischuk (J. ACM'85) where each signature counts as one and where signatures cannot be aggregated nor thresholdized. In this model, we show that partially synchronous consensus under an adaptive adversary requires that honest players send Ω(nt) signatures. We allow randomization, whereas Dolev-Reischuk proved an analogous bound under synchrony for deterministic protocols only.
As a technical contribution, we present a cryptographic formalization of the restricted model of Dolev-Reischuk, which may be of independent interest. We finally turn to the round complexity of randomized BA protocols in which only a subset of parties may speak. We show that such protocols must either rely on erasures or allow a party’s decision whether to speak for the first time to depend on its input. We discuss in detail how both of these design paradigms have been used in prior work and how they lead to efficiency and design-related issues for practical BA protocols.
Cite as
Clément Ducros, Julian Loss, and Matthieu Rambaud. Strong Efficiency Lower Bounds for Byzantine Agreement. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 41:1-41:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{ducros_et_al:LIPIcs.DISC.2026.41,
author = {Ducros, Cl\'{e}ment and Loss, Julian and Rambaud, Matthieu},
title = {{Strong Efficiency Lower Bounds for Byzantine Agreement}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {41:1--41:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.41},
URN = {urn:nbn:de:0030-drops-281478},
doi = {10.4230/LIPIcs.DISC.2026.41},
annote = {Keywords: Byzantine agreement, Byzantine broadcast, communication complexity}
}
Document
Token Distribution Revisited
Abstract
We consider a well-known model for load balancing called token distribution. Starting from an arbitrary distribution of discrete tokens among the nodes of a network, in each time step the edges of a matching are used to transfer at most one token between matched nodes of unequal load. More precisely, if the difference between two matched nodes is at least two, one (and only one) token is moved from the higher-loaded to the lower-loaded node. If the difference is exactly one, this "excess token" is moved with probability 1/2. We prove that for any initial load vector with discrepancy K, our protocol reaches a discrepancy of two in O(K⋅τ_g⋅log log n) rounds with high probability, where τ_g is the balancing time of the continuous diffusion model.
Cite as
Petra Berenbrink, Robert Elsässer, Tom Friedetzky, Hamed Hosseinpour, and Dominik Kaaser. Token Distribution Revisited. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 42:1-42:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{berenbrink_et_al:LIPIcs.DISC.2026.42,
author = {Berenbrink, Petra and Els\"{a}sser, Robert and Friedetzky, Tom and Hosseinpour, Hamed and Kaaser, Dominik},
title = {{Token Distribution Revisited}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {42:1--42:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.42},
URN = {urn:nbn:de:0030-drops-281485},
doi = {10.4230/LIPIcs.DISC.2026.42},
annote = {Keywords: network, load balancing, discrete, token distribution}
}
Document
Multivalued Consensus: General Adversaries Require More Communication
Abstract
We study n-party fault-tolerant consensus against general (non-threshold) adversaries, which are characterized by adversary structures that enumerate every party set Z such that the adversary can corrupt every party in Z. An adversary structure 𝒵 satisfies the 𝒬^d condition if the complete party set [n] is not the union of d or fewer sets in 𝒵. Adversaries characterized by 𝒬^d-satisfying adversary structures generalize threshold adversaries which can corrupt at most t < n/d parties.
For every d ≥ 1, we describe an infinite family 𝒵_proj^{n,d} of 𝒬^d-satisfying n-party adversary structures based on finite projective geometry such that the byzantine adversaries characterized by this family cause error-free R-round protocols for interactive consistency on L-bit inputs (for agreement on every party’s L-bit input) to require Ω(Ln^{2+1/d}) bits of expected communication, if L = Ω(Rn^{-1/d} + 1). Likewise, 𝒵_proj^{n,d} causes byzantine agreement and broadcast to cost Ω(Ln^{1+1/d}) bits, if L = Ω(Rn^{1-1/d}). In every case, the lower bound is Ω(L_{out} ⋅ n^{1+1/d}) bits, where L_{out} is the length of the output. This is in contrast to the case of threshold adversaries, for which the baseline Ω(L_{out} ⋅ n) "every party must learn the output" lower bound is tight for all large L_{out} if the adversary can corrupt Θ(n) parties.
The adversary structure 𝒵_proj^{n,d} also makes Ω(Ln^{1+1/d}) bits of communication required for reliable broadcast and byzantine agreement in asynchronous networks, when L = Ω(n^{1-1/d}). Similarly, there is a family 𝒵_2-proj^{n,d} of 𝒬^d-satisfying adversary structures that cause asynchronous core set agreement to cost Ω(Ln^{2+1/d}) bits. These asynchronous complexity bounds hold against send-omission adversaries, even if the protocol uses cryptography. Their basis is that if a quorum of non-faulty parties agree on an output and terminate, then the messages they sent before terminating must suffice for the parties outside the quorum to also terminate with the same output. Surprisingly, if we do not require the parties to terminate (stop sending messages) after they output, then these lower bounds no longer hold. We show this by designing a non-terminating reliable broadcast protocol for general-omission adversaries that can for any parameter δ > 1 be tuned to cost (1 + 1/(δ-1))Ln + O(δ n²log(δ n)) bits, which is of independent interest. Lastly, we show how to obtain termination with O(L_out ⋅ n^{1+1/d} + n²log n) bits (assuming the 𝒬^d condition), and thus prove our asynchronous lower bounds tight for large L_out.
Cite as
Mose Mizrahi and Roger Wattenhofer. Multivalued Consensus: General Adversaries Require More Communication. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 43:1-43:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{mizrahi_et_al:LIPIcs.DISC.2026.43,
author = {Mizrahi, Mose and Wattenhofer, Roger},
title = {{Multivalued Consensus: General Adversaries Require More Communication}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {43:1--43:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.43},
URN = {urn:nbn:de:0030-drops-281490},
doi = {10.4230/LIPIcs.DISC.2026.43},
annote = {Keywords: Communication Complexity, Lower Bounds, Consensus, Byzantine Agreement, Reliable Broadcast, General Adversary Structures, Byzantine Faults, Omission Faults}
}
Document
Fully Fluctuating Sleepy Consensus from Minimal Assumptions
Abstract
Bitcoin’s proof-of-work (PoW)-based protocol is remarkable for how little it asks of its participants. Not only can miners take breaks from work whenever they please, but it is almost unique in offering a path of contrition: corrupt miners can reclaim honest status simply by resuming mining on the longest chain. The protocol only requires that honest miners hold the majority of computational power at any given time. Analogous proof-of-stake (PoS) protocols, usually formalized via the sleepy model of [Pass and Shi, 2017], have fallen short of matching this robustness. In fact, sleepy consensus protocols in the plain PKI model must heavily restrict fluctuations in adversarial participation over time. The recent work of [Efron et al., 2025] enables fully fluctuating participation in the sleepy model by introducing the external adversary model. Their protocol, however, relies on verifiable delay functions (VDFs), a strong cryptographic primitive that somewhat resembles PoW, by assuming that the adversary cannot compute sequential work significantly faster than honest nodes.
In this work, we design a sleepy consensus protocol for fully fluctuating participation with an external adversary under an honest majority, from minimal assumptions: a public key infrastructure (PKI) and a verifiable random function (VRF). In particular, we make no VDF or hardware assumptions. Our key technique is graded wakeness, a novel primitive that allows nodes to form consistent opinions on which other nodes are awake. We further extend our protocol to handle uncorruption, where corrupt nodes return to honesty. This extension requires only a mild additional assumption on the unpredictability of VRF outputs for liveness.
Cite as
Javier Nieto, Yuval Efron, Joachim Neu, and Ling Ren. Fully Fluctuating Sleepy Consensus from Minimal Assumptions. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 44:1-44:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{nieto_et_al:LIPIcs.DISC.2026.44,
author = {Nieto, Javier and Efron, Yuval and Neu, Joachim and Ren, Ling},
title = {{Fully Fluctuating Sleepy Consensus from Minimal Assumptions}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {44:1--44:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.44},
URN = {urn:nbn:de:0030-drops-281503},
doi = {10.4230/LIPIcs.DISC.2026.44},
annote = {Keywords: Byzantine agreement, proof of stake, sleepy model, fluctuating participation, graded wakeness, verifiable random function}
}
Document
Symmetry All the Way Down
Abstract
Asymmetric trust generalizes classical symmetric quorum systems by allowing each process to specify its own failure assumptions. While this flexibility enables tolerance of strictly more failure scenarios, it is not known if, in these cases, it is actually possible to solve distributed tasks, and if so, which.
We answer this question using the depth hierarchy for asymmetric trust (Amores-Sesar et al., OPODIS '25), which characterizes how much a process must rely on others to solve a task. We prove that asymmetric trust does not increase the solvability of tasks requiring depth two or more, such as reliable broadcast or consensus. Specifically, for any Byzantine asymmetric quorum system, every failure scenario that permits solving a task requiring depth at least two can also be tolerated by a suitably constructed Byzantine symmetric quorum system. We show this via a compiler that transforms asymmetric quorum systems into symmetric ones.
The additional failure patterns tolerated exclusively by asymmetric trust correspond to scenarios in which only simpler tasks requiring depth one or less (such as consistent broadcast) can be solved. We further prove that this result is tight in the depth hierarchy, meaning that there exist no compilers that produce symmetric quorum systems that are valid also in failure scenarios where correct processes have depths one or less.
Our results clarify the precise power of asymmetric trust. While it strictly enlarges the set of tolerable failure patterns, it does not provide additional strength for solving tasks requiring depth two or higher.
Cite as
Ignacio Amores-Sesar, Christian Cachin, Simon Holmgaard Kamp, and Juan Villacis. Symmetry All the Way Down. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 45:1-45:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{amoressesar_et_al:LIPIcs.DISC.2026.45,
author = {Amores-Sesar, Ignacio and Cachin, Christian and Kamp, Simon Holmgaard and Villacis, Juan},
title = {{Symmetry All the Way Down}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {45:1--45:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.45},
URN = {urn:nbn:de:0030-drops-281519},
doi = {10.4230/LIPIcs.DISC.2026.45},
annote = {Keywords: Asymmetric Trust, Quorum Systems, Consensus}
}
Document
Fixed-Threshold Peeling in Sublinear MPC: Round-Approximation Tradeoffs and Applications
Abstract
A number of fundamental graph problems admit simple algorithms based on iterative peeling: repeatedly remove all vertices whose current degree is below a fixed threshold. This paradigm underlies algorithms for density-dependent edge orientation, density-dependent coloring, densest subgraph, and k-core decomposition. In this paper, we study these problems in the sub-linear MPC model.
We achieve the following round-approximation tradeoffs for this family of problems. For any constant δ ∈ (0,1), our algorithms use O(n^δ) local memory and Õ(m+n^{1+δ}) global memory.
- Density-dependent edge orientation. For any integer t > 0, we compute an orientation with maximum out-degree at most (2+ε)(t+1)α(G) in O(lg^{1/(t+2)} n ⋅ poly(lg lg n)) rounds, where α(G) denotes the minimum possible maximum out-degree of an orientation of G. In the poly(lg lg n)-round regime, obtained by setting t = ⌈lg lg n/lg lg lg n⌉, this gives an O(lg lg n/lg lg lg n)-approximation, improving the approximation factor of the recent work by Ghaffari and Grunau [PODC 2025].
- Densest subgraph. We obtain a (4+ε)-approximation in Õ(lg^{1/3} n) MPC rounds and a (6+ε)-approximation in Õ(lg^{1/4} n) MPC rounds. This improves the Õ(√{lg n}) round complexity of Ghaffari, Lattanzi, and Mitrović [ICML 2019] with a slightly larger approximation factor. This is the first O(1)-approximate algorithm for densest subgraph to break the Θ(√{lg n}) round-complexity barrier in the sub-linear MPC model.
- k-core decomposition. For any integer t > 0, we compute approximate coreness values within a factor of (2+ε)(t+1) in O(lg^{1/(t+2)} n ⋅ poly(lg lg n)) MPC rounds. This improves the Õ(√{lg n}) round complexity of Ghaffari, Lattanzi, and Mitrović [ICML 2019], again giving a round-approximation tradeoff.
- Density-dependent coloring. By combining our orientation algorithm with standard coloring reductions, we obtain a coloring with (2+ε)(t+1)α(G)+1 colors in O(lg^{1/(t+2)} n ⋅ poly(lg lg n)) MPC rounds. In particular, this improves the approximation obtainable in poly(lg lg n) rounds over Ghaffari and Grunau [PODC 2025].
Cite as
Slobodan Mitrović, Theodore Pan, and Wen-Horng Sheu. Fixed-Threshold Peeling in Sublinear MPC: Round-Approximation Tradeoffs and Applications. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 46:1-46:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{mitrovic_et_al:LIPIcs.DISC.2026.46,
author = {Mitrovi\'{c}, Slobodan and Pan, Theodore and Sheu, Wen-Horng},
title = {{Fixed-Threshold Peeling in Sublinear MPC: Round-Approximation Tradeoffs and Applications}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {46:1--46:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.46},
URN = {urn:nbn:de:0030-drops-281521},
doi = {10.4230/LIPIcs.DISC.2026.46},
annote = {Keywords: Distributed graph algorithms, Massively Parallel Computation, Densest subgraph, Graph orientation, k-core decomposition, Graph coloring}
}
Document
Accountable MonadBFT: Fast, Responsive, Fork-Resistant Consensus with Speculation Accountability
Abstract
This paper introduces MonadBFT, a novel Byzantine Fault Tolerant (BFT) consensus protocol that advances both performance and robustness. As a HotStuff-family protocol, MonadBFT features linear message and authenticator complexity, where authenticators refer to signatures or partial signatures, on the happy path and is optimistically responsive, operating as quickly as the network allows.
One of the central features of MonadBFT is speculative commitment, which provides the prospective state after three message delays, with reverts occurring only in the rare event of provable leader equivocation. This feature is important for two reasons: first, it decreases the latency for users. Second, it makes MonadBFT resistant to a specific form of Maximal Extractable Value (MEV) attack known as tail-forking. Tail-forking occurs when a malicious leader forks away from its predecessor’s block, causing that block to be abandoned and depriving the predecessor of rewards. This allows the malicious leader to reorder, steal, or exploit transactions, thereby exacerbating MEV exploitation. MonadBFT effectively mitigates such vulnerabilities, ensuring fairness and integrity in transaction processing. To our knowledge, no other pipelined leader-based protocol combines all these features.
To make reverts of speculatively committed blocks even less likely, we extend our protocol to Accountable MonadBFT: whenever a speculatively committed block is reverted, at least one-sixth of all validators are provably culpable, with evidence enabling penalties such as slashing.
Cite as
Mohammad Mussadiq Jalalzai, Kushal Babel, Jovan Komatovic, Tobias Klenze, Sourav Das, Fatima Elsheimy, Mike Setrin, John Bergschneider, and Babak Poorebrahim Gilkalaye. Accountable MonadBFT: Fast, Responsive, Fork-Resistant Consensus with Speculation Accountability. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 47:1-47:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{jalalzai_et_al:LIPIcs.DISC.2026.47,
author = {Jalalzai, Mohammad Mussadiq and Babel, Kushal and Komatovic, Jovan and Klenze, Tobias and Das, Sourav and Elsheimy, Fatima and Setrin, Mike and Bergschneider, John and Gilkalaye, Babak Poorebrahim},
title = {{Accountable MonadBFT: Fast, Responsive, Fork-Resistant Consensus with Speculation Accountability}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {47:1--47:24},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.47},
URN = {urn:nbn:de:0030-drops-281532},
doi = {10.4230/LIPIcs.DISC.2026.47},
annote = {Keywords: BFT consensus, blockchain, speculative commit, accountability}
}
Document
Dynamic Graph Exploration: Semi-Synchrony and Dynamic Port Labeling
Abstract
We study the graph exploration problem in dynamic graphs using mobile agents. We consider 1-interval connected dynamic graphs, where the topology may change arbitrarily from round to round as long as the graph remains connected, and edges are assigned with the dynamic port labeling at each round. The execution follows a semi-synchronous scheduler, under which an adversary may deactivate an arbitrary subset of agents in each round. For a graph with n nodes and k agents, we show that exploration is impossible if the adversary can deactivate at least ⌊(k-1)/(n-2)⌋ agents per round, even when agents are equipped with unbounded memory, have global communication and full visibility. This yields an upper bound, implying that exploration is solvable only when the adversary deactivates at most ⌊(k-1)/(n-2)⌋-1 agents per round. We further establish that achieving exploration at this threshold requires agents to have both 1-hop visibility and 1-hop communication. Finally, we present the exploration algorithm using k agents when the adversary deactivates at most ⌊(k-1)/(n-2)⌋-1 agents, assuming agents are equipped with 1-hop visibility and global communication, and matches the deactivation bound implied by the impossibility results.
Cite as
Ashish Saxena, Anisur Rahaman Molla, Kaushik Mondal, and Gokarna Sharma. Dynamic Graph Exploration: Semi-Synchrony and Dynamic Port Labeling. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 48:1-48:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{saxena_et_al:LIPIcs.DISC.2026.48,
author = {Saxena, Ashish and Molla, Anisur Rahaman and Mondal, Kaushik and Sharma, Gokarna},
title = {{Dynamic Graph Exploration: Semi-Synchrony and Dynamic Port Labeling}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {48:1--48:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.48},
URN = {urn:nbn:de:0030-drops-281540},
doi = {10.4230/LIPIcs.DISC.2026.48},
annote = {Keywords: Mobile agents, Anonymous graphs, Exploration, Dynamic graphs, Semi-synchronous scheduler, Deterministic algorithm}
}
Document
Upper and Lower Bounds on the Space Complexity of Multi-Word Single-Writer Registers
Abstract
We prove matching upper and lower bounds on the space complexity of simulating a large shared register using smaller shared registers. We focus on the case where both the simulated and base registers are single-writer, which means they can be accessed concurrently by multiple readers but only by a single writer. To strengthen our lower bounds, we prove that they hold even when the base registers are atomic and the simulated register is regular. Furthermore, the lower bounds hold for obstruction-free implementations, which means they also hold for lock-free and wait-free implementations.
If m is the number of values representable by the large register and b is the number of values representable by each base register, our first lower bound says that any obstruction-free implementation that has an invisible reader requires at least ⌈(m-1)/(b-1)⌉ base registers. A reader is considered invisible if it never writes to base registers. This lower bound is asymptotically tight for the invisible-reader case and represents an exponential improvement over the previous best known lower bound. For the general case, which allows any combination of visible and invisible readers, we prove a ⌈min(m-1)/(b-1), r + log{m}/log{b})⌉ space lower bound, where r is the number of readers.
To show that this lower bound is asymptotically tight, we develop a wait-free algorithm for simulating a multi-word atomic register from atomic base registers using Θ(r + log{m}/log{b}) space. Combining this algorithm with known invisible-reader constructions gives a Θ(min(m/b, r + log{m}/log{b})) space upper bound. This improves upon the previously known space upper bound of Θ(min(m/b, r log{m}/log{b})).
Cite as
Yuanhao Wei and Yousof Yavari. Upper and Lower Bounds on the Space Complexity of Multi-Word Single-Writer Registers. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 49:1-49:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{wei_et_al:LIPIcs.DISC.2026.49,
author = {Wei, Yuanhao and Yavari, Yousof},
title = {{Upper and Lower Bounds on the Space Complexity of Multi-Word Single-Writer Registers}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {49:1--49:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.49},
URN = {urn:nbn:de:0030-drops-281553},
doi = {10.4230/LIPIcs.DISC.2026.49},
annote = {Keywords: Shared memory, Concurrency, Non-blocking, Multi-word, Register, Space}
}
Document
A Fast Deterministic Algorithm for (Δ + 1)-Edge Coloring in CONGEST
Abstract
Vizing’s theorem states that any graph of maximum degree Δ can be properly edge-colored with Δ + 1 colors (which is optimal in general). A recent breakthrough result by Bernshteyn showed that such a (Δ + 1)-edge coloring can be found deterministically in poly(Δ,log n) rounds in the LOCAL model of distributed computing, where n denotes the number of vertices of the input graph [J. Comb. Theory 2022]. Since then, the exponent in the poly(log n)-part of the runtime has been improved by Christiansen [STOC 2023] and Bernshteyn and Dhawan [J. Comb. Theory, Series B, 2025]. However, the algorithms used in all of these works use large messages, leaving open the question for efficient algorithms in the more restrictive CONGEST model.
We answer this question by presenting the first poly(Δ,log n)-round algorithm for (Δ + 1)-edge coloring in the CONGEST model. Our algorithm is deterministic and the n-dependency of its runtime, Õ(log⁵ n), matches the best published dependency in the LOCAL model.
Cite as
Sebastian Brandt, Ananth Narayanan, and Alexandre Nolin. A Fast Deterministic Algorithm for (Δ + 1)-Edge Coloring in CONGEST. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 50:1-50:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{brandt_et_al:LIPIcs.DISC.2026.50,
author = {Brandt, Sebastian and Narayanan, Ananth and Nolin, Alexandre},
title = {{A Fast Deterministic Algorithm for (\Delta + 1)-Edge Coloring in CONGEST}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {50:1--50:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.50},
URN = {urn:nbn:de:0030-drops-281561},
doi = {10.4230/LIPIcs.DISC.2026.50},
annote = {Keywords: (\Delta + 1)-edge coloring, CONGEST model, deterministic algorithm}
}
Document
Validity in Responsive Byzantine Agreement
Abstract
Byzantine Agreement (BA) protocols must ensure not only agreement and termination, but also validity: the value agreed upon should meaningfully reflect the honest parties' inputs. The choice of validity condition can change the exact resilience threshold at which BA is solvable. Tight characterizations for BA with general validity conditions are known in the partially synchronous model (PODC'23), in the synchronous model (PODC'24), and in the network-agnostic model (DISC'25). Our work focuses on general validity for synchronous BA with responsive termination: such protocols remain secure against up to t_s byzantine corruptions, but incur a running time that depends on the actual network delay δ, rather than the conservative delay bound Δ ≫ δ, whenever at most t_r ≤ t_s parties are corrupted.
We present a tight characterization of the validity properties solvable in this setting. We prove that every non-trivial validity property requires n > 2 t_r+t_s even in authenticated settings (where a public-key infrastructure and digital signatures are available) and n > 3 t_s in unauthenticated settings. These threshold conditions are accompanied by a validity-dependent requirement, the responsive similarity condition: roughly, for any concrete configuration of honest inputs, there is a value that is valid for any view that a protocol could obtain from this initial configuration. We then present matching protocols in both settings, showing that these conditions are sufficient.
The main technical contribution is an authenticated responsive Core-Set Agreement protocol requiring n > 2 t_r+t_s. This threshold may place the protocol in an honest-minority regime, where prior constructions for general validity do not apply and where standard Synchronous Broadcast is not responsive.
Finally, we instantiate the characterization for several standard validity notions - Weak Validity, Strong Unanimity, Convex Validity, and Honest-Input Validity.
Cite as
Diana Ghinea, Simon Holmgaard Kamp, and Chen-Da Liu-Zhang. Validity in Responsive Byzantine Agreement. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 51:1-51:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{ghinea_et_al:LIPIcs.DISC.2026.51,
author = {Ghinea, Diana and Kamp, Simon Holmgaard and Liu-Zhang, Chen-Da},
title = {{Validity in Responsive Byzantine Agreement}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {51:1--51:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.51},
URN = {urn:nbn:de:0030-drops-281573},
doi = {10.4230/LIPIcs.DISC.2026.51},
annote = {Keywords: byzantine agreement, validity, responsive protocols, responsive termination}
}
Document
Near-Tight Bounds on the Rate of Collective Communication
Abstract
Collective communication primitives are used as building blocks in distributed and parallel programming algorithms: they include Broadcast, AllReduce, Gather, and more. These primitives encapsulate aggregation and dissemination tasks, where each host has a data buffer storing a long vector of inputs, and the goal is to aggregate and/or disseminate these inputs in a pointwise manner. Typically, network protocols computing collective communication primitives are implemented over communication networks that use switches to forward messages, and recently also over programmable switches, which may also carry out limited computation.
In this work we study the asymptotic rate of several collective communication primitives: assuming that the capacity of each host-to-switch link suffices to send one input per second, how many instances can we solve per second? We show that in any k-host network that supports both permutation traffic matrices and pipelined serial traffic, the asymptotic rate of the Gather, Scatter, AllGather and AllToAll primitives is ≈ 1/(k-1), while Broadcast and PrefixSum have asymptotic rate ≈ 1. This holds for both forwarding-only and programmable switches. In contrast, for the AllReduce primitive, we show that the rate of computing associative reduction operators in networks with programmable switches is close to 1, while the rate in networks with forwarding-only switches depends on the reduction operator and on the scenario. In particular, for the maximum operator, the rate is close to 1, but the rate of computing integer sums and sums over finite Abelian groups is close to 1/2, even when protocols are allowed randomization, with vanishing {worst-case} error. Moreover, we show that depending on the parameters of the problem, with vanishing distributional error the rate of computing AllReduce of integer sums over forwarding-only switches can be as bad as half the rate afforded by programmable switches, match the rate, or be anywhere in between.
To prove these results we give for the first time sharp general communication-complexity lower bounds for these primitives, using information-theoretic techniques. Prior work on the communication cost of collective communication primitives considered only highly restricted protocols where hosts can only apply reduction operators "as a black box’’; to complement our work, we show this restriction can actually lead to suboptimal throughput - for example, when computing AllReduce with the maximum operator.
Cite as
Rotem Oshman, Tal Roth, Ofer Shayevitz, and Anirudh Sivaraman. Near-Tight Bounds on the Rate of Collective Communication. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 52:1-52:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{oshman_et_al:LIPIcs.DISC.2026.52,
author = {Oshman, Rotem and Roth, Tal and Shayevitz, Ofer and Sivaraman, Anirudh},
title = {{Near-Tight Bounds on the Rate of Collective Communication}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {52:1--52:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.52},
URN = {urn:nbn:de:0030-drops-281580},
doi = {10.4230/LIPIcs.DISC.2026.52},
annote = {Keywords: Programmable switch, communication complexity, information theory}
}
Document
Approximating Minimum Dominating Set with Few Awake Rounds
Abstract
We study the Minimum Dominating Set (MDS) problem in the sleeping Congest model (Chatterjee, Gmyr, and Pandurangan, PODC 2020), a generalization of the standard Congest model, in which a node may sleep in some rounds and can only compute, send messages, or receive messages when it is awake. The awake complexity of an algorithm in this model is the worst case number (over all inputs and all nodes) of rounds a node is awake for during the execution of the algorithm. While there are several O(log Δ)-approximation algorithms (in expectation) for MDS that run in O(log² Δ) rounds, all of these have Ω(log² Δ) awake complexity. Whether this awake complexity can be improved is the question that drives our work. We present the first O(log Δ)-approximation algorithm for MDS with o(log² Δ) awake complexity; our algorithm runs in O(log²Δ) rounds with Õ(logΔ) awake complexity. We can reduce the awake complexity further, but at the cost of approximation: we present, for any 1 < α ≤ Δ, an algorithm in the sleeping Congest model that computes an Õ(αlogΔ)-approximate dominating set in expectation in Õ(logΔ ⋅ log_α Δ) rounds with Õ(log_α Δ) awake complexity. Our results depend on a generalization of the Congest model SetCover algorithm of Grunau, Mitrović, Rubinfeld, and Vakilian (SODA 2020) that we develop. This generalization computes an O(p⋅q⋅log_pΔ)-approximate dominating set in O(log_p Δ ⋅ log_q Δ) rounds for parameters 1 < p,q ≤ Δ. Our sleeping Congest algorithms apply a variety of techniques including sampling-based estimation and scheduling using virtual binary trees to the aforementioned 2-parameter SetCover algorithm.
Cite as
Hongyan Ji, Shreyas Pai, and Sriram V. Pemmaraju. Approximating Minimum Dominating Set with Few Awake Rounds. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 53:1-53:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{ji_et_al:LIPIcs.DISC.2026.53,
author = {Ji, Hongyan and Pai, Shreyas and Pemmaraju, Sriram V.},
title = {{Approximating Minimum Dominating Set with Few Awake Rounds}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {53:1--53:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.53},
URN = {urn:nbn:de:0030-drops-281594},
doi = {10.4230/LIPIcs.DISC.2026.53},
annote = {Keywords: minimum dominating set, sleeping CONGEST, awake complexity, distributed approximation}
}
Document
Weighted Beeping Networks
Abstract
Beeping Networks (BN) have become an established model of wireless communication and computation. They assume, however, that the communication interference caused by beeping nodes is binary (OR channel), while both artificial and nature-driven networks are based on varied signal strength and receiving thresholds. This work naturally extends the classic beeping networks to weighted beeping networks (WBN), by modeling signal strengths by weights on graph edges and receiving a beep if the accumulative signal strengths of transmitting neighbors are above receiving threshold. Under this generalized model, we study the fundamental Local Broadcast (LB) problem. Since edges with low weights may not even accumulate to a received beep, we only require that messages are delivered along sufficiently heavy edges, with weights above some given threshold σ. We design an LB algorithm that completes its task in O(I_σ log n ⋅ (ℳ+log n)) beeping rounds, whp, where n is the number of nodes, I_σ is the maximum local interference on heavy edges, and ℳ is the maximum length of messages sent locally. This result is nearly optimal, as, with probability 1, Ω(I_σ) beeping rounds are necessary to solve LB. Finally, we show that any algorithm designed for the classic beeping networks and terminating in polynomial number of beeping rounds, can be emulated on any WBN with a logarithmic overhead, that is, it returns the same output as working on the classic beeping network isomorphic to the sub-graph of heavy edges.
Cite as
Dariusz R. Kowalski and Miguel A. Mosteiro. Weighted Beeping Networks. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 54:1-54:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{kowalski_et_al:LIPIcs.DISC.2026.54,
author = {Kowalski, Dariusz R. and Mosteiro, Miguel A.},
title = {{Weighted Beeping Networks}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {54:1--54:24},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.54},
URN = {urn:nbn:de:0030-drops-281607},
doi = {10.4230/LIPIcs.DISC.2026.54},
annote = {Keywords: Local Broadcast, Multiagent Systems, Weighted Beeping Networks}
}
Document
Brief Announcement
Brief Announcement: Fast Tendermint: Speeding up a Foundational Consensus Protocol
Abstract
Tendermint is among the most widely studied and deployed Byzantine fault-tolerant (BFT) consensus protocols, owing in part to its native leader-rotation mechanism that subsumes complex view changes. Like most partially-synchronous BFT protocols, Tendermint tolerates f < n/3 Byzantine processes and decides in three communication steps. Motivated by the push for lower-latency blockchains, a recent line of work shows that consensus can be solved in two communication steps when f < n/5. We present Fast Tendermint, an adaptation of Tendermint to the n > 5f setting that decides in two communication steps in the good case, while preserving Tendermint’s leader-rotation structure. Fast Tendermint collapses Tendermint’s prevote and precommit steps into a single voting step and merges the locked and valid state. We give proofs of agreement, validity, and termination, and a formal specification in Quint, a modern surface syntax for TLA^+, used to model-check the protocol.
Cite as
Preston Vander Vos and Daniel Cason. Brief Announcement: Fast Tendermint: Speeding up a Foundational Consensus Protocol. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 55:1-55:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{vandervos_et_al:LIPIcs.DISC.2026.55,
author = {Vander Vos, Preston and Cason, Daniel},
title = {{Brief Announcement: Fast Tendermint: Speeding up a Foundational Consensus Protocol}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {55:1--55:7},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.55},
URN = {urn:nbn:de:0030-drops-281611},
doi = {10.4230/LIPIcs.DISC.2026.55},
annote = {Keywords: BFT consensus, Tendermint, partial synchrony, good-case latency}
}
Document
Brief Announcement
Brief Announcement: Fast TetraBFT - Optimizing Latency Where It Matters
Abstract
Unauthenticated Byzantine consensus protocols achieve optimal failure resilience while relying only on authenticated point-to-point channels, not authenticated messages. They are an attractive building block for blockchains without global trust assumptions as well as for future post-quantum settings. We consider unauthenticated Byzantine consensus in the partial synchrony model and focus on optimizing its good-case latency - the worst-case time for correct processes to reach a decision under favorable conditions. A recently proposed ForgetIT protocol achieves an optimal good-case latency of 3 message delays but employs a highly complex design. We show that this complexity is unnecessary. To this end, we present Fast TetraBFT - an unauthenticated Byzantine consensus protocol that achieves optimal good-case latency by augmenting an existing TetraBFT protocol with a simple fast-path wrapper. Our solution lowers the good-case latency of TetraBFT from 5 to 3 message delays while preserving its bounded space requirements and low communication complexity.
Cite as
Antonio J. Fernández-Pinto, Manuel Bravo, Gregory Chockler, and Alexey Gotsman. Brief Announcement: Fast TetraBFT - Optimizing Latency Where It Matters. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 56:1-56:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{fernandezpinto_et_al:LIPIcs.DISC.2026.56,
author = {Fern\'{a}ndez-Pinto, Antonio J. and Bravo, Manuel and Chockler, Gregory and Gotsman, Alexey},
title = {{Brief Announcement: Fast TetraBFT - Optimizing Latency Where It Matters}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {56:1--56:7},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.56},
URN = {urn:nbn:de:0030-drops-281625},
doi = {10.4230/LIPIcs.DISC.2026.56},
annote = {Keywords: Consensus, partial synchrony, Byzantine fault tolerance}
}
Document
Brief Announcement
Brief Announcement: Semantic Lock: Synchronization Based on the Analysis of the Operation Conflict Graph
Abstract
This paper presents a new lock, SemanticLock, based on the conflict graph between operations. We can consider it a generalization of a read-write lock where conflicts exist between write operations and all other operations.
We demonstrate the effectiveness of our lock in two applications. In the first, we design a toy data structure: an array supporting point queries and different range queries. In the second, potentially of greater interest, we augment an existing concurrent data structure, ConcurrentHashMap, with additional long-running operations.
Cite as
Denis Korotchenko and Vitaly Aksenov. Brief Announcement: Semantic Lock: Synchronization Based on the Analysis of the Operation Conflict Graph. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 57:1-57:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{korotchenko_et_al:LIPIcs.DISC.2026.57,
author = {Korotchenko, Denis and Aksenov, Vitaly},
title = {{Brief Announcement: Semantic Lock: Synchronization Based on the Analysis of the Operation Conflict Graph}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {57:1--57:7},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.57},
URN = {urn:nbn:de:0030-drops-281633},
doi = {10.4230/LIPIcs.DISC.2026.57},
annote = {Keywords: Concurrency, Conflict Graph, Locks, Linearizability, Concurrent Data Structures}
}
Document
Brief Announcement
Brief Announcement: Fair Binding for Hidden-State Authorization in Byzantine SMR
Abstract
Validated Byzantine SMR assumes that replicas can evaluate the validity of an ordered command. Agent authorization creates a different regime: a command may be valid only relative to a committed policy state that validators cannot reconstruct from the log. A proof that an action was authorized at an old commitment is then only a historical attestation, it does not by itself reserve the hidden resource for later use.
We isolate two independent requirements for safe live allocation of a hidden consumable resource under a Byzantine leader. First, arrival order at correct replicas must constrain commit order, the gap addressed by fair-ordering protocols. Second, a committed first request must bind later validity: it must make conflicting later requests invalid, not merely record that the first request was once authorized. The second requirement is non-vacuous precisely because the current policy state is hidden and not prefix-recoverable. Using an explicit authorization-witness interface, we characterize the two distinct obligations in this one-shot reservation model and give a fair reserve/use protocol satisfying both authorization safety and first-arrival liveness. Under trusted FIFO admission the two requirements collapse because admission and execution are atomic, Byzantine SMR separates request commitment from use.
Cite as
Arnab Mallick. Brief Announcement: Fair Binding for Hidden-State Authorization in Byzantine SMR. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 58:1-58:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{mallick:LIPIcs.DISC.2026.58,
author = {Mallick, Arnab},
title = {{Brief Announcement: Fair Binding for Hidden-State Authorization in Byzantine SMR}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {58:1--58:7},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.58},
URN = {urn:nbn:de:0030-drops-281649},
doi = {10.4230/LIPIcs.DISC.2026.58},
annote = {Keywords: Byzantine consensus, validated agreement, order fairness, hidden state, authorization}
}
Document
Brief Announcement
Brief Announcement: Superlogarithmic Gap Result for LCLs on Trees in Quantum-LOCAL
Abstract
We show that, on trees, any locally checkable labeling problem (LCL) Π that can be solved by an n^o(1)-dependent distribution can also be solved by an O(log n)-round deterministic LOCAL algorithm. The result is obtained through a rake-and-compress-style decomposition of the input tree, and local simulations of the bounded dependent distribution on the components of the decomposition. As a corollary to our result, any LCL problem on trees can either be solved by an O(log n) deterministic LOCAL algorithm, or requires n^Ω(1) rounds to solve by a quantum-LOCAL algorithm.
Cite as
Francesco d'Amore and Henrik Lievonen. Brief Announcement: Superlogarithmic Gap Result for LCLs on Trees in Quantum-LOCAL. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 59:1-59:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{damore_et_al:LIPIcs.DISC.2026.59,
author = {d'Amore, Francesco and Lievonen, Henrik},
title = {{Brief Announcement: Superlogarithmic Gap Result for LCLs on Trees in Quantum-LOCAL}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {59:1--59:7},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.59},
URN = {urn:nbn:de:0030-drops-281650},
doi = {10.4230/LIPIcs.DISC.2026.59},
annote = {Keywords: Distributed graph algorithms, LOCAL model, quantum-LOCAL, finitely-dependent distributions, locally checkable labeling problems}
}
Document
Brief Announcement
Brief Announcement: How Complex Can Sequential Consistency Be?
Abstract
Sequential consistency (SC) is the prototypical correctness criterion for shared-memory systems. Deciding whether a finite execution history is SC is NP-complete [Gibbons and Korach, 1997]. In this brief announcement, we study the complexity of SC over infinite execution histories. It is known that SC is not among the safety properties [Glusman and Katz, 2001], which sit at the lowest level of the Borel hierarchy. We show that, under finite arrival, SC is in fact a liveness property. We further demonstrate that no deterministic transducer can compute sequential witnesses for all SC histories, nor can any infinite-state deterministic Büchi acceptor recognize SC. Finally, we establish that, under infinite arrival, SC for memories with unbounded registers and DCAS (double compare-and-swap) is 𝚺¹₁-complete.
Cite as
Dimitar Dimitrov. Brief Announcement: How Complex Can Sequential Consistency Be?. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 60:1-60:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{dimitrov:LIPIcs.DISC.2026.60,
author = {Dimitrov, Dimitar},
title = {{Brief Announcement: How Complex Can Sequential Consistency Be?}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {60:1--60:6},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.60},
URN = {urn:nbn:de:0030-drops-281668},
doi = {10.4230/LIPIcs.DISC.2026.60},
annote = {Keywords: Distributed systems, Consistency, Complexity}
}
Document
Brief Announcement
Brief Announcement: Stone Duality Proofs for Colorless Distributed Computability Theorems
Abstract
Herlihy and Shavit [Herlihy and Shavit, 1999], Saks and Zaharoglou [M. Saks and F. Zaharoglou, 2000], building on the work of Borowsky and Gafni [Borowsky and Gafni, 1997], have shown that questions of distributed computability were amenable to a topological approach by encoding distributed systems as simplicial complexes. We present an extension of the simplicial semantics for distributed computing by identifying spectral topology as a natural generalization thereof. In particular, we extend the topological approach of the Asynchronous Computability Theorem to any round-based, content-neutral, full-information protocol, a family of models containing the Iterated Immediate Snapshot protocol. The main insight of this work is in considering global states obtained after finite executions of a distributed protocol Π not as abstract simplicial complexes as was previously done, but as finite posets.
This extension enables us to prove a new general distributed computability theorem : a protocol Π solves a colorless task (ℐ,𝒪,Δ) if and only if there exists a spectral map f:Π^∞(ℐ) → 𝒪 compatible with Δ, where Π^∞(ℐ) is a spectral space associated to the protocol Π. This space is introduced in this work. From this general characterization, many known colorless computability theorems can be directly derived. In particular, we provide new insights into the previously established connection between colorless task-solvability and continuous maps between geometric realizations. Our proofs rely on Stone duality, a well established tool in semantics theory which links spectral spaces with distributive lattices. In this semantics, spaces correspond to program behaviours and lattices to program specifications, related by a crucial "ingredient" (see [Mai Gehrke, 2016]), namely topology.
Cite as
Cameron Calk and Emmanuel Godard. Brief Announcement: Stone Duality Proofs for Colorless Distributed Computability Theorems. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 61:1-61:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{calk_et_al:LIPIcs.DISC.2026.61,
author = {Calk, Cameron and Godard, Emmanuel},
title = {{Brief Announcement: Stone Duality Proofs for Colorless Distributed Computability Theorems}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {61:1--61:7},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.61},
URN = {urn:nbn:de:0030-drops-281679},
doi = {10.4230/LIPIcs.DISC.2026.61},
annote = {Keywords: simplicial complex, partial order, spectral spaces, Stone duality, categorical semantics}
}
Document
Brief Announcement
Brief Announcement: Simple and Fast Self-Stabilizing Dynamics for k-Winner-Take-All Computation
Abstract
The k-Winner Take All problem consists in identifying the k largest inputs from a collection of input values. We exhibit a simple dynamic network composed of 2n leaky memristor units with a continuous-time dynamics that self-stabilizes and, for any ε > 0, falls within relative distance ε of the k-Winner-Take-All solution on n inputs in time O(ε^{-1} log n).
Cite as
Vincenzo Bonifaci and Fabio Galvan. Brief Announcement: Simple and Fast Self-Stabilizing Dynamics for k-Winner-Take-All Computation. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 62:1-62:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{bonifaci_et_al:LIPIcs.DISC.2026.62,
author = {Bonifaci, Vincenzo and Galvan, Fabio},
title = {{Brief Announcement: Simple and Fast Self-Stabilizing Dynamics for k-Winner-Take-All Computation}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {62:1--62:8},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.62},
URN = {urn:nbn:de:0030-drops-281685},
doi = {10.4230/LIPIcs.DISC.2026.62},
annote = {Keywords: k-Winner-Take-All, network dynamics, nature-inspired distributed algorithms, electrical flows, self-stabilization, distributed optimization, neural leader election, analog computing}
}
Document
Brief Announcement
Brief Announcement: Optimal Adaptive Multi-Valued Byzantine Agreement
Abstract
In Byzantine Agreement (BA), n parties, out of which t can be Byzantine, run a distributed protocol to agree on a common valid input. Traditionally, these protocols have a linear latency and quadratic communication complexity, making them impractical at a large scale. In their recent work, Constantinescu, Dufay, Paramonov, and Wattenhofer [PODC'26] consider the actual number of byzantine parties f ≤ t and work toward decoupling the dependency on n and t in the complexity. They obtain a BA protocol with 𝒪̃(n + t⋅f) communication complexity and 𝒪̃(f) round complexity.
However, their results are strictly limited to agreement on a binary value. Using the framework given by their work along with novel techniques, we extend these results for BA on an L-bit value. With κ being a security parameter, and with optimal resiliency (t < n/2 in the synchronous setting or t < n/3 otherwise), we obtain:
- In synchrony, a deterministic protocol with 𝒪(n⋅ (L + f⋅κ)) bit complexity and 𝒪(f + log n) round complexity.
- In synchrony and partial synchrony, deterministic protocols with 𝒪̃(n⋅κ + t⋅ (L + f⋅κ)) bit complexity and 𝒪(f) round complexity.
- In asynchrony, a protocol with 𝒪̃(n ⋅ κ + t⋅(L + t⋅κ)) expected bit complexity and expected 𝒪(1) latency.
Cite as
Marc Dufay, Anton Paramonov, and Roger Wattenhofer. Brief Announcement: Optimal Adaptive Multi-Valued Byzantine Agreement. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 63:1-63:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{dufay_et_al:LIPIcs.DISC.2026.63,
author = {Dufay, Marc and Paramonov, Anton and Wattenhofer, Roger},
title = {{Brief Announcement: Optimal Adaptive Multi-Valued Byzantine Agreement}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {63:1--63:7},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.63},
URN = {urn:nbn:de:0030-drops-281698},
doi = {10.4230/LIPIcs.DISC.2026.63},
annote = {Keywords: Byzantine Agreement, Communication Complexity, Adaptive Communication Complexity, Resilience}
}
Document
Brief Announcement
Brief Announcement: Liquid Democracy Under Vote Correlation: On the Fallacies of Averaging and the Excluded Middle
Abstract
Liquid democracy permits voters either to vote directly or to delegate their votes to others. Existing algorithmic analyses usually assign each voter a single scalar competence parameter, representing an independent probability of voting for the ground truth. This representation is inadequate when delegation is fixed before later public information changes different voters' reliability in different ways. In this work, we study a minimal common-signal model of this realistic phenomenon. Delegation occurs before a public binary signal is realised, while voting occurs afterwards. Conditional on the signal, sink votes are independent and each voter has a signal-specific competence; marginally, correctness events are correlated through the common signal. We show that delegation based on average competence is not a safe scalarisation. We then present three novel delegation mechanisms for this setting. We analyse and show the precise conditions under which our mechanisms inherit delegation desiderata, as well as outline the tradeoffs between these mechanisms.
Cite as
Seth Gilbert, Stefan Schmid, Santiago Schnell, Jakub Svoboda, and Michelle X. Yeo. Brief Announcement: Liquid Democracy Under Vote Correlation: On the Fallacies of Averaging and the Excluded Middle. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 64:1-64:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{gilbert_et_al:LIPIcs.DISC.2026.64,
author = {Gilbert, Seth and Schmid, Stefan and Schnell, Santiago and Svoboda, Jakub and Yeo, Michelle X.},
title = {{Brief Announcement: Liquid Democracy Under Vote Correlation: On the Fallacies of Averaging and the Excluded Middle}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {64:1--64:6},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.64},
URN = {urn:nbn:de:0030-drops-281701},
doi = {10.4230/LIPIcs.DISC.2026.64},
annote = {Keywords: Liquid democracy, Voting, Delegation, Mechanism design, Distributed algorithms}
}
Document
Brief Announcement
Brief Announcement: Initialization with Exponentially Fewer Bits
Abstract
One of the most fundamental challenges in radio networks is avoiding collisions during communication. This is especially important in single-hop radio networks, where only a single processor is able to transmit at a time. To overcome this obstacle, the processors, which we assume are indistinguishable to begin with, solve initialization. That is, they each get assigned distinct numbers from 1 to n. Because collisions occur if two or more processors transmit simultaneously, solving initialization requires Ω(n) rounds, and O(n) round protocols have long been known.
These networks are often made up of battery-powered devices, meaning energy is a crucial resource. We therefore consider a model in which nodes are allowed to sleep to save energy at the expense of communicating. Previous work by Nakano and Olariu [Nakano and Olariu, 2000] showed that initialization can be solved in O(log log n) energy using O(log n)-bit messages. We first show that their energy bound is optimal, giving a lower bound that Ω(log log n) sends are needed by any initialization protocol whose round complexity is nearly quasilinear in n. In the more restrictive setting without sender- or receiver-side collision detection (no-CD Model), we show that we can initialize all but a small fraction f of nodes with an energy complexity that depends only on f. As a corollary, we obtain the first constant-energy algorithm for initializing 0.999n nodes.
We then consider the setting in which messages are limited to single bits. In this case, we present a series of improvements that result in an algorithm in which each node sends and receives up to O(log log n) bits - exponentially fewer than all previous work. Ultimately, we show that this can be done in O(n) single-bit rounds, with a worst-case bit complexity of O(log log n) and a node-averaged bit complexity of O(1).
Cite as
Dominick Banasik, Varsha Dani, and Thomas P. Hayes. Brief Announcement: Initialization with Exponentially Fewer Bits. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 65:1-65:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{banasik_et_al:LIPIcs.DISC.2026.65,
author = {Banasik, Dominick and Dani, Varsha and Hayes, Thomas P.},
title = {{Brief Announcement: Initialization with Exponentially Fewer Bits}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {65:1--65:7},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.65},
URN = {urn:nbn:de:0030-drops-281713},
doi = {10.4230/LIPIcs.DISC.2026.65},
annote = {Keywords: Distributed Computing, Energy Complexity, Radio Networks, Initialization}
}
Document
Brief Announcement
Brief Announcement: Simulations Between Massively Parallel Computing and Distributed Computing
Abstract
We study how the Massively Parallel Computation (MPC) model in the strongly sublinear regime relates to graph-centric distributed models, focusing on the Node-Capacitated Clique (NCC), a bandwidth-parametrized generalization of the Congested Clique. In MPC, M machines with per-machine memory S hold a partition of the input graph. In NCC, we are given n nodes that are themselves machines that know their full neighborhood but can send and receive at most C words per round. We are interested in the strongly sublinear regime where S = n^δ, for some constant 0 < δ < 1 and C = MS/n, for which no prior simulation results are known.
We explore when deterministic round-preserving simulations between these models are possible and when they are provably not, for different model parameters, problem families and graph classes. On the positive side, we provide techniques that allow, under certain restrictions, simulations with only constant overhead. On the negative side, we prove simulation impossibility results, which show that the limitations of our simulation results are inherent.
Cite as
Philipp Schneider and Julian Werthmann. Brief Announcement: Simulations Between Massively Parallel Computing and Distributed Computing. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 66:1-66:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{schneider_et_al:LIPIcs.DISC.2026.66,
author = {Schneider, Philipp and Werthmann, Julian},
title = {{Brief Announcement: Simulations Between Massively Parallel Computing and Distributed Computing}},
booktitle = {40th International Symposium on Distributed Computing (DISC 2026)},
pages = {66:1--66:7},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-454-3},
ISSN = {1868-8969},
year = {2026},
volume = {397},
editor = {Moses Jr., William K. and Censor-Hillel, Keren},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2026.66},
URN = {urn:nbn:de:0030-drops-281720},
doi = {10.4230/LIPIcs.DISC.2026.66},
annote = {Keywords: Model simulations, massively parallel computation, node capacitated clique}
}