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DOI: 10.4230/LIPIcs.SWAT.2026.35

Path-Reporting Distance Oracles for Vertex-Labeled Graphs

Authors: Ofer Neiman and Alon Spector

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract

Let G = (V,E) be a weighted undirected graph, with n vertices. A distance oracle is a data structure that can quickly answer distance queries, with some stretch factor. A seminal work of [Thorup and Zwick, 2005], given an integer k ≥ 1, provides such an oracle with stretch 2k-1, query time O(k), and size O(k⋅ n^{1+1/k}). Furthermore, this oracle can also report a path in G corresponding to the returned distance. In this paper we focus on vertex-labeled graphs, in which each vertex is given a label from a set L of size 𝓁. A vertex-label distance oracle answers queries of the form (v,λ), where v ∈ V and λ ∈ L, by reporting (an approximation to) the distance from v to the closest vertex of label λ. Following [Danny Hermelin et al., 2011], it was shown in [Chechik, 2012] that for any integer k > 1, there exists a vertex-label distance oracle with stretch 4k-5, query time O(k), and size O(k⋅ n⋅ 𝓁^{1/k}). This state-of-the-art result suffers from two main drawbacks: The stretch is roughly a factor of 2 larger than in [Thorup and Zwick, 2005], and it is not path-reporting. We address these concerns in this work, and provide the following results. - First, we devise a path-reporting vertex-label distance oracle, at the cost of a slight increase in stretch and size. For any constant 0 < ε < 1, our oracle has stretch (4k-5)⋅(1+ε), query time O(k), and size O(n^{1+o(1)}⋅ 𝓁^{1/k}). - Second, we show how to improve the stretch to the optimal 2k-1, at the cost of mildly increasing the query time. Specifically, we devise a vertex-label distance oracle with stretch 2k-1, query time O(𝓁^{1/k}⋅log n), and size O(k⋅ n⋅ 𝓁^{1/k}).

Cite as

Ofer Neiman and Alon Spector. Path-Reporting Distance Oracles for Vertex-Labeled Graphs. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{neiman_et_al:LIPIcs.SWAT.2026.35,
  author =	{Neiman, Ofer and Spector, Alon},
  title =	{{Path-Reporting Distance Oracles for Vertex-Labeled Graphs}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{35:1--35:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.35},
  URN =		{urn:nbn:de:0030-drops-260719},
  doi =		{10.4230/LIPIcs.SWAT.2026.35},
  annote =	{Keywords: Graph Algorithms, Shortest Paths, Distance Oracles}
}

Document

DOI: 10.4230/LIPIcs.FORC.2026.22

Separating Oblivious and Adaptive Differential Privacy Under Continual Observation

Authors: Mark Bun, Marco Gaboardi, and Connor Wagaman

Published in: LIPIcs, Volume 368, 7th Symposium on Foundations of Responsible Computing (FORC 2026)

Abstract

We resolve an open question of Jain, Raskhodnikova, Sivakumar, and Smith (ICML 2023) by exhibiting a problem separating differential privacy under continual observation in the oblivious and adaptive settings. The continual observation (a.k.a. continual release) model formalizes privacy for streaming algorithms, where data is received over time and output is released at each time step. In the oblivious setting, privacy need only hold for data streams fixed in advance; in the adaptive setting, privacy is required even for streams that can be chosen adaptively based on the streaming algorithm’s output. We describe the first explicit separation between the oblivious and adaptive settings. The problem showing this separation is based on the correlated vector queries problem of Bun, Steinke, and Ullman (SODA 2017). Specifically, we present an (ε,0)-DP algorithm for the oblivious setting that remains accurate for exponentially many time steps in the dimension of the input. On the other hand, we show that every (ε,δ)-DP adaptive algorithm fails to be accurate after releasing output for only a constant number of time steps.

Cite as

Mark Bun, Marco Gaboardi, and Connor Wagaman. Separating Oblivious and Adaptive Differential Privacy Under Continual Observation. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 22:1-22:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bun_et_al:LIPIcs.FORC.2026.22,
  author =	{Bun, Mark and Gaboardi, Marco and Wagaman, Connor},
  title =	{{Separating Oblivious and Adaptive Differential Privacy Under Continual Observation}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{22:1--22:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-419-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{368},
  editor =	{Lin, Huijia (Rachel)},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2026.22},
  URN =		{urn:nbn:de:0030-drops-259959},
  doi =		{10.4230/LIPIcs.FORC.2026.22},
  annote =	{Keywords: differential privacy, continual observation, continual release, streaming algorithms, adaptive algorithms}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2026.64

Gap-ETH-Tight Algorithms for Hyperbolic TSP and Steiner Tree

Authors: Sándor Kisfaludi-Bak, Saeed Odak, Satyam Singh, and Geert van Wordragen

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract

We give an approximation scheme for the TSP in d-dimensional hyperbolic space that has optimal dependence on ε under Gap-ETH. For any fixed dimension d ≥ 2 and for any ε > 0 our randomized algorithm gives a (1+ε)-approximation in time 2^O(1/ε^{d-1}) n^{1+o(1)}. We also provide an algorithm for the hyperbolic Steiner tree problem with the same running time. Our algorithm is an Arora-style dynamic program based on a randomly shifted hierarchical decomposition. However, we introduce a new hierarchical decomposition called the hybrid hyperbolic quadtree to achieve the desired large-scale structure, which deviates significantly from the recently proposed hyperbolic quadtree of Kisfaludi-Bak and Van Wordragen (JoCG'25). Moreover, we have a new non-uniform portal placement, and our structure theorem employs a new weighted crossing analysis. We believe that these techniques could form the basis for further developments in geometric optimization in curved spaces.

Cite as

Sándor Kisfaludi-Bak, Saeed Odak, Satyam Singh, and Geert van Wordragen. Gap-ETH-Tight Algorithms for Hyperbolic TSP and Steiner Tree. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 64:1-64:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kisfaludibak_et_al:LIPIcs.SoCG.2026.64,
  author =	{Kisfaludi-Bak, S\'{a}ndor and Odak, Saeed and Singh, Satyam and van Wordragen, Geert},
  title =	{{Gap-ETH-Tight Algorithms for Hyperbolic TSP and Steiner Tree}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{64:1--64:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.64},
  URN =		{urn:nbn:de:0030-drops-258710},
  doi =		{10.4230/LIPIcs.SoCG.2026.64},
  annote =	{Keywords: Hyperbolic traveling salesman problem, TSP, Hyperbolic Steiner tree problem, Approximation scheme, Banyan, Hyperbolic geometry}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2026.65

Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces

Authors: Sándor Kisfaludi-Bak and Geert van Wordragen

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract

We consider Steiner spanners in Euclidean and non-Euclidean geometries. In the Euclidean setting, a recent line of work initiated by Le and Solomon [FOCS'19] and further improved by Chang et al. [SoCG'24] obtained Steiner (1+ε)-spanners of size O_d(ε^{(1-d)/2} log(1/ε) n), nearly matching the lower bound Ω_d(ε^{(1-d)/2} n) of Bhore and Tóth [SIDMA'22]. We obtain Steiner (1+ε)-spanners of size O_d(ε^{(1-d)/2} log(1/ε)n) not only in d-dimensional Euclidean space, but also in d-dimensional spherical and hyperbolic space. For any fixed dimension d, the obtained edge count is optimal up to an O(log(1/ε)) factor in each of these spaces. Unlike earlier constructions, our Steiner spanners are based on simple quadtrees, and they can be dynamically maintained, leading to efficient data structures for dynamic approximate nearest neighbours and bichromatic closest pair. In the hyperbolic setting, we also show that 2-spanners in the hyperbolic plane must have Ω(nlog n) edges, and we obtain a 2-spanner of size O_d(nlog n) in d-dimensional hyperbolic space, matching our lower bound for any constant d. Finally, we give a Steiner spanner with additive error ε in hyperbolic space with O_d(ε^{(1-d)/2} log(α(n)/ε)n) edges, where α(n) is the inverse Ackermann function. Our techniques generalize to closed orientable surfaces of constant curvature as well as to some other quotient spaces.

Cite as

Sándor Kisfaludi-Bak and Geert van Wordragen. Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 65:1-65:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kisfaludibak_et_al:LIPIcs.SoCG.2026.65,
  author =	{Kisfaludi-Bak, S\'{a}ndor and van Wordragen, Geert},
  title =	{{Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{65:1--65:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.65},
  URN =		{urn:nbn:de:0030-drops-258728},
  doi =		{10.4230/LIPIcs.SoCG.2026.65},
  annote =	{Keywords: hyperbolic geometry, Steiner spanner, dynamic approximate nearest neighbours}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2026.68

Optimal Bounds for Spanners and Tree Covers in Doubling Metrics

Authors: An La, Hung Le, Shay Solomon, Cuong Than, Vinayak, Shuang Yang, and Tianyi Zhang

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract

It is known that any n-point set in the d-dimensional Euclidean space ℝ^d, for d = O(1), admits: 1) A (1+ε)-spanner with maximum degree Õ(ε^{-d+1}) and with lightness Õ(ε^{-d}), for any ε > 0. 2) A (1+ε)-tree cover with Õ(n ⋅ ε^{-d+1}) trees and maximum degree of O(1) in each tree. Moreover, all the parameters in these constructions are optimal: For any 2 ≤ d = O(1), there exists an n-point set in ℝ^d, for which any (1+ε)-spanner has Ω̃(n⋅ε^{-d+1}) edges and lightness Ω̃(ε^{-d}). The upper bounds for Euclidean spanners rely heavily on the spatial property of cone partitioning in ℝ^d, which does not seem to extend to the wider family of doubling metrics, i.e., metric spaces of constant doubling dimension. In doubling metrics, a simple spanner construction from two decades ago, the net-tree spanner, has Õ(n⋅ε^{-d}) edges, and it could be transformed into a spanner of maximum degree Õ(ε^{-d}) and lightness Õ(n⋅ε^{-(d+1)}) by pruning redundant edges. Moreover, a careful refinement of the net-tree spanner yields a (1+ε)-tree cover with Õ(ε^{-d}) trees. Despite a large body of work, the problem of obtaining tight bounds for spanners and tree covers in the wider family of doubling metrics has remained elusive. We resolve this problem by presenting: 1) A surprisingly simple and tight lower bound, which shows that the net-tree spanner and its pruned version are optimal with respect to all the involved parameters. 2) A new construction of (1+ε)-tree covers with Õ(n⋅ε^{-d}) trees, with maximum degree O(1) in each tree. This construction is optimal with respect to the number of trees and maximum degree.

Cite as

An La, Hung Le, Shay Solomon, Cuong Than, Vinayak, Shuang Yang, and Tianyi Zhang. Optimal Bounds for Spanners and Tree Covers in Doubling Metrics. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 68:1-68:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{la_et_al:LIPIcs.SoCG.2026.68,
  author =	{La, An and Le, Hung and Solomon, Shay and Than, Cuong and Vinayak and Yang, Shuang and Zhang, Tianyi},
  title =	{{Optimal Bounds for Spanners and Tree Covers in Doubling Metrics}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{68:1--68:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.68},
  URN =		{urn:nbn:de:0030-drops-258756},
  doi =		{10.4230/LIPIcs.SoCG.2026.68},
  annote =	{Keywords: doubling metrics, doubling spanners, Euclidean spanners, tree cover}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2026.13

Dynamic Light Spanners in Doubling Metrics

Authors: Sujoy Bhore, Jonathan Conroy, and Arnold Filtser

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract

A t-spanner of a point set X in a metric space (𝒳, δ) is a graph G with vertex set P such that, for any pair of points u,v ∈ X, the distance between u and v in G is at most t times δ(u,v). We study the problem of maintaining a spanner for a dynamic point set X - that is, when X undergoes a sequence of insertions and deletions - in a metric space of constant doubling dimension. For any constant ε > 0, we maintain a (1+ε)-spanner of P whose total weight remains within a constant factor of the weight of the minimum spanning tree of X. Each update (insertion or deletion) can be performed in poly(log Φ) time, where Φ denotes the aspect ratio of X. Prior to our work, no efficient dynamic algorithm for maintaining a light-weight spanner was known even for point sets in low-dimensional Euclidean space.

Cite as

Sujoy Bhore, Jonathan Conroy, and Arnold Filtser. Dynamic Light Spanners in Doubling Metrics. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bhore_et_al:LIPIcs.SoCG.2026.13,
  author =	{Bhore, Sujoy and Conroy, Jonathan and Filtser, Arnold},
  title =	{{Dynamic Light Spanners in Doubling Metrics}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{13:1--13:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.13},
  URN =		{urn:nbn:de:0030-drops-258193},
  doi =		{10.4230/LIPIcs.SoCG.2026.13},
  annote =	{Keywords: Dynamic data structures, spanners, light-weight, Euclidean metrics, doubling metrics}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.38

Lower Bounds on Tree Covers

Authors: Yu Chen, Zihan Tan, and Hangyu Xu

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract

Given an n-point metric space (X,d_X), a tree cover 𝒯 is a set of |𝒯| = k trees on X such that every pair of vertices in X has a low-distortion path in one of the trees in 𝒯. Tree covers have been playing a crucial role in graph algorithms for decades, and the research focus is the construction of tree covers with small size k and distortion. When k = 1, the best distortion is known to be Θ(n). For a constant k ≥ 2, the best distortion upper bound is Õ(n^{1/k}) and the strongest lower bound is Ω(log_k n), leaving a gap to be closed. In this paper, we improve the lower bound to Ω(n^{1/(2^{k-1)}}). Our proof is a novel analysis on a structurally simple grid-like graph, which utilizes some combinatorial fixed-point theorems. We believe that they will prove useful for analyzing other tree-like data structures as well.

Cite as

Yu Chen, Zihan Tan, and Hangyu Xu. Lower Bounds on Tree Covers. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 38:1-38:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chen_et_al:LIPIcs.ITCS.2026.38,
  author =	{Chen, Yu and Tan, Zihan and Xu, Hangyu},
  title =	{{Lower Bounds on Tree Covers}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{38:1--38:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.38},
  URN =		{urn:nbn:de:0030-drops-253254},
  doi =		{10.4230/LIPIcs.ITCS.2026.38},
  annote =	{Keywords: Tree Covers, Combinatorial Fixed-Point Theorems}
}

Document

DOI: 10.4230/LIPIcs.OPODIS.2025.16

Asynchronous Approximate Agreement with Quadratic Communication

Authors: Mose Mizrahi Erbes and Roger Wattenhofer

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract

We study approximate agreement in an asynchronous network of n parties, up to t of which are byzantine. This an agreement task where the parties obtain approximately equal inputs in the convex hull of their inputs. In an asynchronous network, it can be solved with the optimal resilience t < n/3 by forcing the parties to reliably broadcast their messages and thus preventing inconsistent byzantine behavior. This costs Θ(n²) messages per reliable broadcast, or Θ(n³) messages per protocol iteration. In this work, we forgo reliable broadcast to achieve asynchronous approximate agreement against t < n/3 faults with quadratic communication. In a tree with the maximum degree Δ and the centroid decomposition height h, we achieve edge agreement (agreement on two adjacent vertices) in at most 6h + 1 rounds with 𝒪(n²) messages of size 𝒪(log Δ + log h) per round. We do this by designing a 6-round multivalued 2-graded consensus protocol and using it to construct a recursive edge agreement protocol. Then, we achieve edge agreement in the infinite path ℤ, again by using 2-graded consensus. Finally, we show that our edge agreement protocol enables approximate agreement in ℝ (with outputs that are at most some small parameter ε > 0 apart) in 6log₂M/(ε) + 𝒪(log log M/(ε)) rounds with 𝒪(n²) messages of size 𝒪(log log M/(ε)) per round, where M is the maximum non-byzantine input magnitude.

Cite as

Mose Mizrahi Erbes and Roger Wattenhofer. Asynchronous Approximate Agreement with Quadratic Communication. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 16:1-16:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mizrahierbes_et_al:LIPIcs.OPODIS.2025.16,
  author =	{Mizrahi Erbes, Mose and Wattenhofer, Roger},
  title =	{{Asynchronous Approximate Agreement with Quadratic Communication}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{16:1--16:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.16},
  URN =		{urn:nbn:de:0030-drops-251890},
  doi =		{10.4230/LIPIcs.OPODIS.2025.16},
  annote =	{Keywords: Approximate agreement, byzantine fault tolerance, communication complexity}
}

Document

DOI: 10.4230/LIPIcs.DISC.2025.1

ABEL: Perfect Asynchronous Byzantine Extension from List-Decoding

Authors: Ittai Abraham and Gilad Asharov

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract

Asynchronous byzantine agreement extension studies the message complexity of L-bit multivalued asynchronous byzantine agreement given access to a binary asynchronous Byzantine agreement protocol. We prove that asynchronous byzantine agreement extension can be solved with perfect security and optimal resilience in O(nL+n² log n) total communication (in bits) in addition to a single call to a binary asynchronous Byzantine agreement protocol. For L = O(n log n), this gives an asymptotically optimal protocol, resolving a question that remained open for nearly two decades. List decoding is a fundamental concept in theoretical computer science and cryptography, enabling error correction beyond the unique decoding radius and playing a critical role in constructing robust codes, hardness amplification, and secure cryptographic protocols. A key novelty of our perfectly secure and optimally resilient asynchronous byzantine agreement extension protocol is that it uses list decoding - making a striking new connection between list decoding and asynchronous Byzantine agreement.

Cite as

Ittai Abraham and Gilad Asharov. ABEL: Perfect Asynchronous Byzantine Extension from List-Decoding. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{abraham_et_al:LIPIcs.DISC.2025.1,
  author =	{Abraham, Ittai and Asharov, Gilad},
  title =	{{ABEL: Perfect Asynchronous Byzantine Extension from List-Decoding}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.1},
  URN =		{urn:nbn:de:0030-drops-248185},
  doi =		{10.4230/LIPIcs.DISC.2025.1},
  annote =	{Keywords: Asynchronous Byzantine Agreement, Perfect Security}
}

Document

Brief Announcement

DOI: 10.4230/LIPIcs.DISC.2025.61

Brief Announcement: Asynchronous Approximate Agreement with Quadratic Communication

Authors: Mose Mizrahi Erbes and Roger Wattenhofer

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract

We consider an asynchronous network of n message-sending parties, up to t of which are byzantine. We study approximate agreement, where the parties obtain approximately equal outputs in the convex hull of their inputs. In their seminal work, Abraham, Amit and Dolev [OPODIS '04] solve this problem in ℝ with the optimal resilience t < n/3 with a protocol where each party reliably broadcasts a value in every iteration. This takes Θ(n²) messages per reliable broadcast, or Θ(n³) messages per iteration. In this work, we forgo reliable broadcast to achieve asynchronous approximate agreement against t < n/3 faults with quadratic communication. In a tree with the maximum degree Δ and the centroid decomposition height h, we achieve edge agreement in at most 6h + 1 rounds with 𝒪(n²) messages of size 𝒪(log Δ + log h) per round. We do this by designing a 6-round multivalued 2-graded consensus protocol and using it to recursively reduce the task to edge agreement in a subtree with a smaller centroid decomposition height. Then, we achieve edge agreement in the infinite path ℤ, again with the help of 2-graded consensus. Finally, we show that our edge agreement protocol enables ε-agreement in ℝ in 6log₂M/(ε) + 𝒪(log log M/(ε)) rounds with 𝒪(n² log M/(ε)) messages and 𝒪(n²log M/(ε)log log M/(ε)) bits of communication, where M is the maximum non-byzantine input magnitude.

Cite as

Mose Mizrahi Erbes and Roger Wattenhofer. Brief Announcement: Asynchronous Approximate Agreement with Quadratic Communication. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 61:1-61:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mizrahierbes_et_al:LIPIcs.DISC.2025.61,
  author =	{Mizrahi Erbes, Mose and Wattenhofer, Roger},
  title =	{{Brief Announcement: Asynchronous Approximate Agreement with Quadratic Communication}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{61:1--61:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.61},
  URN =		{urn:nbn:de:0030-drops-248771},
  doi =		{10.4230/LIPIcs.DISC.2025.61},
  annote =	{Keywords: Approximate agreement, byzantine fault tolerance, communication complexity}
}

Document

Brief Announcement

DOI: 10.4230/LIPIcs.DISC.2025.52

Brief Announcement: From Few to Many Faults: Adaptive Byzantine Agreement with Optimal Communication

Authors: Andrei Constantinescu, Marc Dufay, Anton Paramonov, and Roger Wattenhofer

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract

We study the problem of Strong Byzantine Agreement and establish tight upper and lower bounds on communication complexity, parameterized by the actual number of Byzantine faults. Specifically, for a system of n parties tolerating up to t Byzantine faults, out of which only f ≤ t are actually faulty, we obtain the following results: In the partially synchronous setting, we present the first Byzantine Agreement protocol that achieves adaptive communication complexity of 𝒪(n + t ⋅ f) words, which is asymptotically optimal. Our protocol has an optimal resilience of t < n/3. In the asynchronous setting, we prove a lower bound of Ω(n + t²) on the expected number of messages, and design an almost matching protocol with an optimal resilience that solves agreement with 𝒪((n + t²)⋅ log n) words. Our main technical contribution in the asynchronous setting is the utilization of a bipartite expander graph that allows for low-cost information dissemination.

Cite as

Andrei Constantinescu, Marc Dufay, Anton Paramonov, and Roger Wattenhofer. Brief Announcement: From Few to Many Faults: Adaptive Byzantine Agreement with Optimal Communication. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 52:1-52:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{constantinescu_et_al:LIPIcs.DISC.2025.52,
  author =	{Constantinescu, Andrei and Dufay, Marc and Paramonov, Anton and Wattenhofer, Roger},
  title =	{{Brief Announcement: From Few to Many Faults: Adaptive Byzantine Agreement with Optimal Communication}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{52:1--52:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.52},
  URN =		{urn:nbn:de:0030-drops-248680},
  doi =		{10.4230/LIPIcs.DISC.2025.52},
  annote =	{Keywords: Byzantine Agreement, Communication Complexity, Adaptive Communication Complexity, Resilience}
}

Document

DOI: 10.4230/LIPIcs.AFT.2025.7

Mechanism Design for Automated Market Makers

Authors: T-H. Hubert Chan, Ke Wu, and Elaine Shi

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract

Blockchains have popularized automated market makers (AMMs), applications that run on a blockchain, maintain a pool of crypto-assets, and execute trades with users governed by some pricing function. AMMs have also introduced a significant challenge known as the Miner Extractable Value (MEV). Specifically, miners who control the contents and sequencing of transactions in a block can extract value by front-running and back-running users' transactions, creating arbitrage opportunities that guarantee them risk-free returns. MEV not only harms ordinary users, but more critically, encourages miners to auction off favorable transaction placements to users and arbitragers. This has fostered a more centralized off-chain eco-system, departing from the decentralized equilibrium originally envisioned for the blockchain infrastructure layer. In this paper, we consider how to design AMM mechanisms that eliminate MEV opportunities. Specifically, we propose a new AMM mechanism that processes all transactions contained within a block according to some pre-defined rules, ensuring that some constant potential function is maintained after processing the batch. We show that our new mechanism satisfies two tiers of guarantees. First, for legacy blockchains where each block is proposed by a single (possibly rotating) miner, we prove that our mechanism satisfies arbitrage resilience, i.e., a miner cannot gain risk-free profit. Second, for blockchains where the block proposal process is decentralized and offers sequencing-fairness, we prove a strictly stronger notion called strategy proofness - roughly speaking, we guarantee that any individual user’s best response is to follow the honest strategy. Our results complement prior works on MEV resilience in the following senses. First, prior works have shown impossibilities to address MEV entirely at the consensus level. Our work demonstrates a new paradigm of mechanism design at the application (i.e., smart contract) layer to ensure provable guarantees of strategy proofness. Second, many works have attempted to augment the underlying consensus protocol with extra properties such as sequencing fairness. While most previous works heuristically argued why these extra properties help to mitigate MEV, our work demonstrates in a mathematically formal manner how to leverage such consensus-level properties to aid the design of strategy-proof mechanisms.

Cite as

T-H. Hubert Chan, Ke Wu, and Elaine Shi. Mechanism Design for Automated Market Makers. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chan_et_al:LIPIcs.AFT.2025.7,
  author =	{Chan, T-H. Hubert and Wu, Ke and Shi, Elaine},
  title =	{{Mechanism Design for Automated Market Makers}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{7:1--7:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.7},
  URN =		{urn:nbn:de:0030-drops-247265},
  doi =		{10.4230/LIPIcs.AFT.2025.7},
  annote =	{Keywords: Mechanism design, game theory, strategy proof, blockchain}
}

Document

DOI: 10.4230/LIPIcs.AFT.2025.18

From Permissioned to Proof-of-Stake Consensus

Authors: Jovan Komatovic, Andrew Lewis-Pye, Joachim Neu, Tim Roughgarden, and Ertem Nusret Tas

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract

This paper presents the first generic compiler that transforms any permissioned consensus protocol into a proof-of-stake permissionless consensus protocol. For each of the following properties, if the initial permissioned protocol satisfies that property in the partially synchronous setting, the consequent proof-of-stake protocol also satisfies that property in the partially synchronous and quasi-permissionless setting (with the same fault-tolerance): consistency; liveness; optimistic responsiveness; every composable log-specific property; and message complexity of a given order. Moreover, our transformation ensures that the output protocol satisfies accountability (identifying culprits in the event of a consistency violation), whether or not the original permissioned protocol satisfied it.

Cite as

Jovan Komatovic, Andrew Lewis-Pye, Joachim Neu, Tim Roughgarden, and Ertem Nusret Tas. From Permissioned to Proof-of-Stake Consensus. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 18:1-18:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{komatovic_et_al:LIPIcs.AFT.2025.18,
  author =	{Komatovic, Jovan and Lewis-Pye, Andrew and Neu, Joachim and Roughgarden, Tim and Tas, Ertem Nusret},
  title =	{{From Permissioned to Proof-of-Stake Consensus}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{18:1--18:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.18},
  URN =		{urn:nbn:de:0030-drops-247373},
  doi =		{10.4230/LIPIcs.AFT.2025.18},
  annote =	{Keywords: Permissioned Consensus, Proof-of-Stake, generic Compiler, Blockchain}
}

Document

DOI: 10.4230/LIPIcs.AFT.2025.12

How Much Public Randomness Do Modern Consensus Protocols Need?

Authors: Joseph Bonneau, Benedikt Bünz, Miranda Christ, and Yuval Efron

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract

Modern blockchain-based consensus protocols aim for efficiency (i.e., low communication and round complexity) while maintaining security against adaptive adversaries. These goals are usually achieved using a public randomness beacon to select roles for each participant. We examine to what extent this randomness is necessary. Specifically, we provide tight bounds on the amount of entropy a Byzantine Agreement protocol must consume from a beacon in order to enjoy efficiency and adaptive security. We first establish that no consensus protocol can simultaneously be efficient, be adaptively secure, and use O(log n) bits of beacon entropy. We then show this bound is tight and, in fact, a trilemma by presenting three consensus protocols that achieve any two of these three properties.

Cite as

Joseph Bonneau, Benedikt Bünz, Miranda Christ, and Yuval Efron. How Much Public Randomness Do Modern Consensus Protocols Need?. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 12:1-12:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonneau_et_al:LIPIcs.AFT.2025.12,
  author =	{Bonneau, Joseph and B\"{u}nz, Benedikt and Christ, Miranda and Efron, Yuval},
  title =	{{How Much Public Randomness Do Modern Consensus Protocols Need?}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{12:1--12:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.12},
  URN =		{urn:nbn:de:0030-drops-247310},
  doi =		{10.4230/LIPIcs.AFT.2025.12},
  annote =	{Keywords: Consensus, Randomness Beacon}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.ESA.2025.2

Securing Dynamic Data: A Primer on Differentially Private Data Structures (Invited Talk)

Authors: Monika Henzinger and Roodabeh Safavi

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract

We give an introduction into differential privacy in the dynamic setting, called the continual observation setting.

Cite as

Monika Henzinger and Roodabeh Safavi. Securing Dynamic Data: A Primer on Differentially Private Data Structures (Invited Talk). In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 2:1-2:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{henzinger_et_al:LIPIcs.ESA.2025.2,
  author =	{Henzinger, Monika and Safavi, Roodabeh},
  title =	{{Securing Dynamic Data: A Primer on Differentially Private Data Structures}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{2:1--2:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.2},
  URN =		{urn:nbn:de:0030-drops-244702},
  doi =		{10.4230/LIPIcs.ESA.2025.2},
  annote =	{Keywords: Differential privacy, continual observation}
}

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