17 Search Results for "Rapaport, Ivan"

Document
DOI: 10.4230/LIPIcs.OPODIS.2025.26
Recognizing Hereditary Properties in the Presence of Byzantine Nodes

Authors: David Cifuentes-Núñez, Pedro Montealegre, and Ivan Rapaport

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

Abstract
Augustine et al. [DISC 2022] initiated the study of distributed graph algorithms in the presence of Byzantine nodes in the congested clique model. In this model, there is a set B of Byzantine nodes, where |B| is less than a third of the total number of nodes. These nodes have complete knowledge of the network and the state of other nodes, and they conspire to alter the output of the system. The authors addressed the connectivity problem, showing that it is solvable under the promise that either the subgraph induced by the honest nodes is connected, or the graph has 2|B|+1 connected components. In the current work, we continue the study of the Byzantine congested clique model by considering the recognition of other graph properties, specifically hereditary properties. A graph property is hereditary if it is closed under taking induced subgraphs. Examples of hereditary properties include acyclicity, bipartiteness, planarity, and bounded (chromatic, independence) number, etc. For each class of graphs 𝒢 satisfying a hereditary property (a hereditary graph-class), we propose a randomized algorithm which, with high probability, (1) accepts if the input graph G belongs to 𝒢, and (2) rejects if G contains at least |B| + 1 disjoint subgraphs not belonging to 𝒢. The round complexity of our algorithm is 𝒪(((log (|𝒢_n|))/n) +|B|) ⋅polylog(n)) , where 𝒢_n is the set of n-node graphs in 𝒢. Finally, we obtain an impossibility result that proves that our result is tight. Indeed, we consider the hereditary class of acyclic graphs, and we prove that there is no algorithm that can distinguish between a graph being acyclic and a graph having |B| disjoint cycles.
Cite as

David Cifuentes-Núñez, Pedro Montealegre, and Ivan Rapaport. Recognizing Hereditary Properties in the Presence of Byzantine Nodes. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cifuentesnunez_et_al:LIPIcs.OPODIS.2025.26,
  author =	{Cifuentes-N\'{u}\~{n}ez, David and Montealegre, Pedro and Rapaport, Ivan},
  title =	{{Recognizing Hereditary Properties in the Presence of Byzantine Nodes}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{26:1--26:15},
  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.2025.26},
  URN =		{urn:nbn:de:0030-drops-251990},
  doi =		{10.4230/LIPIcs.OPODIS.2025.26},
  annote =	{Keywords: Byzantine protocols, congested clique, hereditary properties}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.17
Treedepth Inapproximability and Exponential ETH Lower Bound

Authors: Édouard Bonnet, Daniel Neuen, and Marek Sokołowski

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Treedepth is a central parameter to algorithmic graph theory. The current state-of-the-art in computing and approximating treedepth consists of a 2^{O(k²)} n-time exact algorithm and a polynomial-time O(OPT log^{3/2} OPT)-approximation algorithm, where the former algorithm returns an elimination forest of height k (witnessing that treedepth is at most k) for the n-vertex input graph G, or correctly reports that G has treedepth larger than k, and OPT is the actual value of the treedepth. On the complexity side, exactly computing treedepth is NP-complete, but the known reductions do not rule out a polynomial-time approximation scheme (PTAS), and under the Exponential Time Hypothesis (ETH) only exclude a running time of 2^o(√n) for exact algorithms. We show that 1.0003-approximating Treedepth is NP-hard, and that exactly computing the treedepth of an n-vertex graph requires time 2^Ω(n), unless the ETH fails. We further derive that there exist absolute constants δ, c > 0 such that any (1+δ)-approximation algorithm requires time 2^Ω(n/log^c n). We do so via a simple direct reduction from Satisfiability to Treedepth, inspired by a reduction recently designed for Treewidth [STOC '25].
Cite as

Édouard Bonnet, Daniel Neuen, and Marek Sokołowski. Treedepth Inapproximability and Exponential ETH Lower Bound. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 17:1-17:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonnet_et_al:LIPIcs.IPEC.2025.17,
  author =	{Bonnet, \'{E}douard and Neuen, Daniel and Soko{\l}owski, Marek},
  title =	{{Treedepth Inapproximability and Exponential ETH Lower Bound}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{17:1--17:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.17},
  URN =		{urn:nbn:de:0030-drops-251494},
  doi =		{10.4230/LIPIcs.IPEC.2025.17},
  annote =	{Keywords: treedepth, lower bounds, approximation}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.51
Distributed Complexity of P_k-Freeness: Decision and Certification

Authors: Masayuki Miyamoto

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
The class of graphs that do not contain a path on k nodes as an induced subgraph (P_k-free graphs) has rich applications in the theory of graph algorithms. This paper explores the problem of deciding P_k-freeness from the viewpoint of distributed computing. For specific small values of k, we present the first CONGEST algorithms specified for P_k-freeness, utilizing structural properties of P_k-free graphs in a novel way. Specifically, we show that P_k-freeness can be decided in Õ(1) rounds for k = 4 in the broadcast CONGEST model, and in Õ(n) rounds for k = 5 in the CONGEST model, where n is the number of nodes in the network and Õ(⋅) hides a polylog(n) factor. The main technical contribution is a novel technique used in our algorithm for P₅-freeness to distinguish induced 5-paths from non-induced ones, which is potentially applicable to other induced subgraphs. This technique also enables the construction of a local certification of P₅-freeness with certificates of size Õ(n). This improves Õ(n^{3/2}) by Bousquet and Zeitoun (TCS 2025), and is nearly optimal, given our Ω(n^{1-o(1)}) lower bound on certificate size. For general k, we establish the first CONGEST lower bound, which is of the form n^{2-1/Θ(k)}. The n^{1/Θ(k)} factor is unavoidable, in view of the O(n^{2-2/(3k+2)}) upper bound by Eden et al. (Dist. Comp. 2022). Additionally, our approach yields the first superlinear lower bound on certificate size for local certification. This partially answers the conjecture on the optimal certificate size of P_k-freeness, asked by Bousquet et al. (arXiv:2402.12148). Finally, we propose a novel variant of the problem called ordered P_k detection. We show that in the CONGEST model, the round complexity of ordered P_k detection is Ω̃(n) for k ≥ 5, and in contrast, proving any nontrivial lower bound for ordered P₃ detection implies a strong circuit lower bound. As a byproduct, we establish a circuit-complexity barrier for Ω(n^{1/2+ε}) quantum CONGEST lower bounds for induced 4-cycle detection. This is complemented by our Õ(n^{3/4}) quantum upper bound, which surpasses the classical Ω̃(n) lower bound by Le Gall and Miyamoto (ISAAC 2021).
Cite as

Masayuki Miyamoto. Distributed Complexity of P_k-Freeness: Decision and Certification. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 51:1-51:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{miyamoto:LIPIcs.ISAAC.2025.51,
  author =	{Miyamoto, Masayuki},
  title =	{{Distributed Complexity of P\underlinek-Freeness: Decision and Certification}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{51:1--51:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.51},
  URN =		{urn:nbn:de:0030-drops-249597},
  doi =		{10.4230/LIPIcs.ISAAC.2025.51},
  annote =	{Keywords: subgraph detection, CONGEST model, local certification}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.22
The Complexity Landscape of Dynamic Distributed Subgraph Finding

Authors: Yi-Jun Chang, Lyuting Chen, Yanyu Chen, Gopinath Mishra, and Mingyang Yang

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

Abstract
Bonne and Censor-Hillel (ICALP 2019) initiated the study of distributed subgraph finding in dynamic networks of limited bandwidth. For the case where the target subgraph is a clique, they determined the tight bandwidth complexity bounds in nearly all settings. However, several open questions remain, and very little is known about finding subgraphs beyond cliques. In this work, we consider these questions and explore subgraphs beyond cliques in the deterministic setting. For finding cliques, we establish an Ω(log log n) bandwidth lower bound for one-round membership-detection under edge insertions only and an Ω(log log log n) bandwidth lower bound for one-round detection under both edge insertions and node insertions. Moreover, we demonstrate new algorithms to show that our lower bounds are tight in bounded-degree networks when the target subgraph is a triangle. Prior to our work, no lower bounds were known for these problems. For finding subgraphs beyond cliques, we present a complete characterization of the bandwidth complexity of the membership-listing problem for every target subgraph, every number of rounds, and every type of topological change: node insertions, node deletions, edge insertions, and edge deletions. We also show partial characterizations for one-round membership-detection and listing.
Cite as

Yi-Jun Chang, Lyuting Chen, Yanyu Chen, Gopinath Mishra, and Mingyang Yang. The Complexity Landscape of Dynamic Distributed Subgraph Finding. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chang_et_al:LIPIcs.DISC.2025.22,
  author =	{Chang, Yi-Jun and Chen, Lyuting and Chen, Yanyu and Mishra, Gopinath and Yang, Mingyang},
  title =	{{The Complexity Landscape of Dynamic Distributed Subgraph Finding}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{22:1--22:20},
  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.2025.22},
  URN =		{urn:nbn:de:0030-drops-248399},
  doi =		{10.4230/LIPIcs.DISC.2025.22},
  annote =	{Keywords: Distributed algorithms, dynamic algorithms, subgraph finding}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.20
Two for One, One for All: Deterministic LDC-Based Robust Computation in Congested Clique

Authors: Keren Censor-Hillel, Orr Fischer, Ran Gelles, and Pedro Soto

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

Abstract
We design a deterministic compiler that makes any computation in the Congested Clique model robust to a constant fraction α < 1 of adversarial crash faults. In particular, we show how a network of n nodes can compute any circuit of depth d, width ω, and gate total fan Δ, in d ⋅ ⌈ω/n² + Δ/n⌉ ⋅ 2^{O(√{log{n}}log log{n})} rounds in such a faulty model. As a corollary, any T-round Congested Clique algorithm can be compiled into an algorithm that completes in T² n^{o(1)} rounds in this model. Our compiler obtains resilience to node crashes by coding information across the network, and its main underlying observation is that we can leverage locally-decodable codes (LDCs) to maintain a low complexity overhead, as these allow recovering the information needed at each computational step by querying only small parts of the codeword, instead of retrieving the entire coded message, which is inherent when using block codes. The main technical contribution is that because erasures occur in known locations, which correspond to crashed nodes, we can derandomize classical LDC constructions by deterministically selecting query sets that avoid sufficiently many erasures. Moreover, when decoding multiple codewords in parallel, our derandomization load-balances the queries per-node, thereby preventing congestion and maintaining a low round complexity. Deterministic decoding of LDCs presents a new challenge: the adversary can target precisely the (few) nodes that are queried for decoding a certain codeword. We overcome this issue via an adaptive doubling strategy: if a decoding attempt for a codeword fails, the node doubles the number of its decoding attempts. We employ a similar doubling technique when the adversary crashes the decoding node itself, replacing it dynamically with two other non-crashed nodes. By carefully combining these two doubling processes, we overcome the challenges posed by the combination of a deterministic LDC with a worst case pattern of crashes.
Cite as

Keren Censor-Hillel, Orr Fischer, Ran Gelles, and Pedro Soto. Two for One, One for All: Deterministic LDC-Based Robust Computation in Congested Clique. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{censorhillel_et_al:LIPIcs.DISC.2025.20,
  author =	{Censor-Hillel, Keren and Fischer, Orr and Gelles, Ran and Soto, Pedro},
  title =	{{Two for One, One for All: Deterministic LDC-Based Robust Computation in Congested Clique}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{20:1--20:19},
  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.2025.20},
  URN =		{urn:nbn:de:0030-drops-248379},
  doi =		{10.4230/LIPIcs.DISC.2025.20},
  annote =	{Keywords: Congested Clique, Fault Tolerance, Error Correction Codes}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.18
Complexity Landscape for Local Certification

Authors: Nicolas Bousquet, Laurent Feuilloley, and Sébastien Zeitoun

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

Abstract
An impressive recent line of work has charted the complexity landscape of distributed graph algorithms. For many settings, it has been determined which time complexities exist, and which do not (in the sense that no local problem could have an optimal algorithm with that complexity). In this paper, we initiate the study of the landscape for space complexity of distributed graph algorithms. More precisely, we focus on the local certification setting, where a prover assigns certificates to nodes to certify a property, and where the space complexity is measured by the size of the certificates. Already for anonymous paths and cycles, we unveil a surprising landscape: - There is a gap between complexity O(1) and Θ(log log n) in paths. This is the first gap established in local certification. - There exists a property that has complexity Θ(log log n) in paths, a regime that was not known to exist for a natural property. - There is a gap between complexity O(1) and Θ(log n) in cycles, hence a gap that is exponentially larger than for paths. We then generalize our result for paths to the class of trees. Namely, we show that there is a gap between complexity O(1) and Θ(log log d) in trees, where d is the diameter. We finally describe some settings where there are no gaps at all. To prove our results we develop a new toolkit, based on various results of automata theory and arithmetic, which is of independent interest.
Cite as

Nicolas Bousquet, Laurent Feuilloley, and Sébastien Zeitoun. Complexity Landscape for Local Certification. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 18:1-18:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bousquet_et_al:LIPIcs.DISC.2025.18,
  author =	{Bousquet, Nicolas and Feuilloley, Laurent and Zeitoun, S\'{e}bastien},
  title =	{{Complexity Landscape for Local Certification}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{18:1--18:21},
  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.2025.18},
  URN =		{urn:nbn:de:0030-drops-248350},
  doi =		{10.4230/LIPIcs.DISC.2025.18},
  annote =	{Keywords: Local certification, proof-labeling schemes, locally checkable proofs, space complexity, distributed graph algorithms, complexity gap}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.34
New Distributed Interactive Proofs for Planarity: A Matter of Left and Right

Authors: Yuval Gil and Merav Parter

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

Abstract
We provide new distributed interactive proofs (DIP) for planarity and related graph families. The notion of a distributed interactive proof (DIP) was introduced by Kol, Oshman, and Saxena (PODC 2018). In this setting, the verifier consists of n nodes connected by a communication graph G. The prover is a single entity that communicates with all nodes by short messages. The goal is to verify that the graph G satisfies a certain property (e.g., planarity) in a small number of rounds, and with a small communication bound, denoted as the proof size. Prior work by Naor, Parter and Yogev (SODA 2020) presented a DIP for planarity that uses three interaction rounds and a proof size of O(log n). Feuilloley et al. (PODC 2020) showed that the same can be achieved with a single interaction round and without randomization, by providing a proof labeling scheme with a proof size of O(log n). In a subsequent work, Bousquet, Feuilloley, and Pierron (OPODIS 2021) achieved the same bound for related graph families such as outerplanarity, series-parallel graphs, and graphs of treewidth at most 2. In this work, we design new DIPs that use exponentially shorter proofs compared to the state-of-the-art bounds. Our main results are: - There is a 5-round protocol with O(log log n) proof size for outerplanarity. - There is a 5-round protocol with O(log log n) proof size for verifying embedded planarity and O(log log n+log Δ) proof size for general planar graphs, where Δ is the maximum degree in the graph. In the former setting, it is assumed that an embedding of the graph is given (e.g., each node holds a clockwise orientation of its neighbors) and the goal is to verify that it is a valid planar embedding. The latter result should be compared with the non-interactive setting for which there is lower bound of Ω(log n) bits for graphs with Δ = O(1) by Feuilloley et al. (PODC 2020). - The non-interactive deterministic lower bound of Ω(log n) bits by Feuilloley et al. (PODC 2020) can be extended to hold even if the verifier is randomized. Moreover, the lower bound holds even with the assumption that the verifier’s randomness comes in the form of an unbounded random string shared among the nodes. We also show that our DIPs can be extended to protocols with similar bounds for verifying series-parallel graphs and graphs with tree-width at most 2. Perhaps surprisingly, our results demonstrate that the key technical barrier for obtaining o(log log n) labels for all our problems is a basic sorting verification task in which all nodes are embedded on an oriented path P ⊆ G and it is desired for each node to distinguish between its left and right G-neighbors.
Cite as

Yuval Gil and Merav Parter. New Distributed Interactive Proofs for Planarity: A Matter of Left and Right. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 34:1-34:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gil_et_al:LIPIcs.DISC.2025.34,
  author =	{Gil, Yuval and Parter, Merav},
  title =	{{New Distributed Interactive Proofs for Planarity: A Matter of Left and Right}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{34:1--34:23},
  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.2025.34},
  URN =		{urn:nbn:de:0030-drops-248515},
  doi =		{10.4230/LIPIcs.DISC.2025.34},
  annote =	{Keywords: Distributed interactive proofs, Planar graphs}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.20
Routing Few Robots in a Crowded Network

Authors: Argyrios Deligkas, Eduard Eiben, Robert Ganian, Iyad Kanj, Dominik Leko, and M. S. Ramanujan

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
In Graph Coordinated Motion Planning, we are given a graph G some of whose vertices are occupied by robots, and we are asked to route k marked robots to their destinations while avoiding collisions and without exceeding a given budget 𝓁 on the number of robot moves. We continue the recent investigation of the problem [ICALP 2024], focusing on the parameter k that captures the task of routing a small number of robots in a possibly crowded graph. We prove that the problem is W[1]-hard parameterized by 𝓁 even for k = 1, but fixed-parameter tractable parameterized by k plus the treedepth of G. We complement the latter algorithm with an NP-hardness reduction which shows that both parameters are necessary to achieve tractability.
Cite as

Argyrios Deligkas, Eduard Eiben, Robert Ganian, Iyad Kanj, Dominik Leko, and M. S. Ramanujan. Routing Few Robots in a Crowded Network. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{deligkas_et_al:LIPIcs.WADS.2025.20,
  author =	{Deligkas, Argyrios and Eiben, Eduard and Ganian, Robert and Kanj, Iyad and Leko, Dominik and Ramanujan, M. S.},
  title =	{{Routing Few Robots in a Crowded Network}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{20:1--20:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.20},
  URN =		{urn:nbn:de:0030-drops-242516},
  doi =		{10.4230/LIPIcs.WADS.2025.20},
  annote =	{Keywords: graph coordinated motion planning, parameterized complexity, treedepth}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.16
Shared Randomness Helps with Local Distributed Problems

Authors: Alkida Balliu, Mohsen Ghaffari, Fabian Kuhn, Augusto Modanese, Dennis Olivetti, Mikaël Rabie, Jukka Suomela, and Jara Uitto

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
By prior work, we have many wonderful results related to distributed graph algorithms for problems that can be defined with local constraints; the formal framework used in prior work is locally checkable labeling problems (LCLs), introduced by Naor and Stockmeyer in the 1990s. It is known, for example, that if we have a deterministic algorithm that solves an LCL in o(log n) rounds, we can speed it up to O(log^* n) rounds, and if we have a randomized algorithm that solves an LCL in O(log^* n) rounds, we can derandomize it for free. It is also known that randomness helps with some LCL problems: there are LCL problems with randomized complexity Θ(log log n) and deterministic complexity Θ(log n). However, so far there have not been any LCL problems in which the use of shared randomness has been necessary; in all prior algorithms it has been enough that the nodes have access to their own private sources of randomness. Could it be the case that shared randomness never helps with LCLs? Could we have a general technique that takes any distributed graph algorithm for any LCL that uses shared randomness, and turns it into an equally fast algorithm where private randomness is enough? In this work we show that the answer is no. We present an LCL problem Π such that the round complexity of Π is Ω(√n) in the usual randomized LOCAL model (with private randomness), but if the nodes have access to a source of shared randomness, then the complexity drops to O(log n). As corollaries, we also resolve several other open questions related to the landscape of distributed computing in the context of LCL problems. In particular, problem Π demonstrates that distributed quantum algorithms for LCL problems strictly benefit from a shared quantum state. Problem Π also gives a separation between finitely dependent distributions and non-signaling distributions.
Cite as

Alkida Balliu, Mohsen Ghaffari, Fabian Kuhn, Augusto Modanese, Dennis Olivetti, Mikaël Rabie, Jukka Suomela, and Jara Uitto. Shared Randomness Helps with Local Distributed Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balliu_et_al:LIPIcs.ICALP.2025.16,
  author =	{Balliu, Alkida and Ghaffari, Mohsen and Kuhn, Fabian and Modanese, Augusto and Olivetti, Dennis and Rabie, Mika\"{e}l and Suomela, Jukka and Uitto, Jara},
  title =	{{Shared Randomness Helps with Local Distributed Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.16},
  URN =		{urn:nbn:de:0030-drops-233931},
  doi =		{10.4230/LIPIcs.ICALP.2025.16},
  annote =	{Keywords: Distributed computing, locally checkable labelings, shared randomness}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2024.26
The Singular Optimality of Distributed Computation in LOCAL

Authors: Fabien Dufoulon, Gopal Pandurangan, Peter Robinson, and Michele Scquizzato

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
It has been shown that one can design distributed algorithms that are (nearly) singularly optimal, meaning they simultaneously achieve optimal time and message complexity (within polylogarithmic factors), for several fundamental global problems such as broadcast, leader election, and spanning tree construction, under the KT₀ assumption. With this assumption, nodes have initial knowledge only of themselves, not their neighbors. In this case the time and message lower bounds are Ω(D) and Ω(m), respectively, where D is the diameter of the network and m is the number of edges, and there exist (even) deterministic algorithms that simultaneously match these bounds. On the other hand, under the KT₁ assumption, whereby each node has initial knowledge of itself and the identifiers of its neighbors, the situation is not clear. For the KT₁ CONGEST model (where messages are of small size), King, Kutten, and Thorup (KKT) showed that one can solve several fundamental global problems (with the notable exception of BFS tree construction) such as broadcast, leader election, and spanning tree construction with Õ(n) message complexity (n is the network size), which can be significantly smaller than m. Randomization is crucial in obtaining this result. While the message complexity of the KKT result is near-optimal, its time complexity is Õ(n) rounds, which is far from the standard lower bound of Ω(D). An important open question is whether one can achieve singular optimality for the above problems in the KT₁ CONGEST model, i.e., whether there exists an algorithm running in Õ(D) rounds and Õ(n) messages. Another important and related question is whether the fundamental BFS tree construction can be solved with Õ(n) messages (regardless of the number of rounds as long as it is polynomial in n) in KT₁. In this paper, we show that in the KT₁ LOCAL model (where message sizes are not restricted), singular optimality is achievable. Our main result is that all global problems, including BFS tree construction, can be solved in Õ(D) rounds and Õ(n) messages, where both bounds are optimal up to polylogarithmic factors. Moreover, we show that this can be achieved deterministically.
Cite as

Fabien Dufoulon, Gopal Pandurangan, Peter Robinson, and Michele Scquizzato. The Singular Optimality of Distributed Computation in LOCAL. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dufoulon_et_al:LIPIcs.OPODIS.2024.26,
  author =	{Dufoulon, Fabien and Pandurangan, Gopal and Robinson, Peter and Scquizzato, Michele},
  title =	{{The Singular Optimality of Distributed Computation in LOCAL}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{26:1--26:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.26},
  URN =		{urn:nbn:de:0030-drops-225629},
  doi =		{10.4230/LIPIcs.OPODIS.2024.26},
  annote =	{Keywords: Distributed algorithms, round and message complexity, BFS tree construction, leader election}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2024.34
Quantum Simultaneous Protocols Without Public Coins Using Modified Equality Queries

Authors: François Le Gall, Oran Nadler, Harumichi Nishimura, and Rotem Oshman

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
In this paper we study a quantum version of the multiparty simultaneous message-passing (SMP) model, and we show that in some cases, quantum communication can replace public randomness, even with no entanglement between the parties. This was already known for two players, but not for more than two players, and indeed, so far all that was known was a negative result. Our main technical contribution is a compiler that takes any classical public-coin simultaneous protocol based on "modified equality queries," and converts it into a quantum simultaneous protocol without public coins with roughly the same communication complexity. We then use our compiler to derive protocols for several problems, including frequency moments, neighborhood diversity, enumeration of isolated cliques, and more.
Cite as

François Le Gall, Oran Nadler, Harumichi Nishimura, and Rotem Oshman. Quantum Simultaneous Protocols Without Public Coins Using Modified Equality Queries. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 34:1-34:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{legall_et_al:LIPIcs.OPODIS.2024.34,
  author =	{Le Gall, Fran\c{c}ois and Nadler, Oran and Nishimura, Harumichi and Oshman, Rotem},
  title =	{{Quantum Simultaneous Protocols Without Public Coins Using Modified Equality Queries}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{34:1--34:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.34},
  URN =		{urn:nbn:de:0030-drops-225701},
  doi =		{10.4230/LIPIcs.OPODIS.2024.34},
  annote =	{Keywords: SMP model, multi-party communication, quantum distributed algorithms}
}
Document
DOI: 10.4230/LIPIcs.DISC.2024.25
Distributed Model Checking on Graphs of Bounded Treedepth

Authors: Fedor V. Fomin, Pierre Fraigniaud, Pedro Montealegre, Ivan Rapaport, and Ioan Todinca

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)

Abstract
We establish that every monadic second-order logic (MSO) formula on graphs with bounded treedepth is decidable in a constant number of rounds within the CONGEST model. To our knowledge, this marks the first meta-theorem regarding distributed model-checking. Various optimization problems on graphs are expressible in MSO. Examples include determining whether a graph G has a clique of size k, whether it admits a coloring with k colors, whether it contains a graph H as a subgraph or minor, or whether terminal vertices in G could be connected via vertex-disjoint paths. Our meta-theorem significantly enhances the work of Bousquet et al. [PODC 2022], which was focused on distributed certification of MSO on graphs with bounded treedepth. Moreover, our results can be extended to solving optimization and counting problems expressible in MSO, in graphs of bounded treedepth.
Cite as

Fedor V. Fomin, Pierre Fraigniaud, Pedro Montealegre, Ivan Rapaport, and Ioan Todinca. Distributed Model Checking on Graphs of Bounded Treedepth. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fomin_et_al:LIPIcs.DISC.2024.25,
  author =	{Fomin, Fedor V. and Fraigniaud, Pierre and Montealegre, Pedro and Rapaport, Ivan and Todinca, Ioan},
  title =	{{Distributed Model Checking on Graphs of Bounded Treedepth}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{25:1--25:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.25},
  URN =		{urn:nbn:de:0030-drops-212513},
  doi =		{10.4230/LIPIcs.DISC.2024.25},
  annote =	{Keywords: proof-labeling schemes, local computing, CONGEST model}
}
Document
DOI: 10.4230/LIPIcs.DISC.2023.20
Distributed Certification for Classes of Dense Graphs

Authors: Pierre Fraigniaud, Frédéric Mazoit, Pedro Montealegre, Ivan Rapaport, and Ioan Todinca

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)

Abstract
A proof-labeling scheme (PLS) for a boolean predicate Π on labeled graphs is a mechanism used for certifying the legality with respect to Π of global network states in a distributed manner. In a PLS, a certificate is assigned to each processing node of the network, and the nodes are in charge of checking that the collection of certificates forms a global proof that the system is in a correct state, by exchanging the certificates once, between neighbors only. The main measure of complexity is the size of the certificates. Many PLSs have been designed for certifying specific predicates, including cycle-freeness, minimum-weight spanning tree, planarity, etc. In 2021, a breakthrough has been obtained, as a "meta-theorem" stating that a large set of properties have compact PLSs in a large class of networks. Namely, for every MSO₂ property Π on labeled graphs, there exists a PLS for Π with O(log n)-bit certificates for all graphs of bounded tree-depth. This result has been extended to the larger class of graphs with bounded tree-width, using certificates on O(log² n) bits. We extend this result even further, to the larger class of graphs with bounded clique-width, which, as opposed to the other two aforementioned classes, includes dense graphs. We show that, for every MSO₁ property Π on labeled graphs, there exists a PLS for Π with O(log² n)-bit certificates for all graphs of bounded clique-width. As a consequence, certifying families of graphs such as distance-hereditary graphs and (induced) P₄-free graphs (a.k.a., cographs) can be done using a PLS with O(log² n)-bit certificates, merely because each of these two classes can be specified in MSO₁. In fact, we show that certifying P₄-free graphs can be done with certificates on O(log n) bits only. This is in contrast to the class of C₄-free graphs (which does not have bounded clique-width) which requires Ω̃(√n)-bit certificates.
Cite as

Pierre Fraigniaud, Frédéric Mazoit, Pedro Montealegre, Ivan Rapaport, and Ioan Todinca. Distributed Certification for Classes of Dense Graphs. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fraigniaud_et_al:LIPIcs.DISC.2023.20,
  author =	{Fraigniaud, Pierre and Mazoit, Fr\'{e}d\'{e}ric and Montealegre, Pedro and Rapaport, Ivan and Todinca, Ioan},
  title =	{{Distributed Certification for Classes of Dense Graphs}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{20:1--20:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.20},
  URN =		{urn:nbn:de:0030-drops-191467},
  doi =		{10.4230/LIPIcs.DISC.2023.20},
  annote =	{Keywords: CONGEST, Proof Labelling Schemes, clique-width, MSO}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2022.20
Computing Power of Hybrid Models in Synchronous Networks

Authors: Pierre Fraigniaud, Pedro Montealegre, Pablo Paredes, Ivan Rapaport, Martín Ríos-Wilson, and Ioan Todinca

Published in: LIPIcs, Volume 253, 26th International Conference on Principles of Distributed Systems (OPODIS 2022)

Abstract
During the last two decades, a small set of distributed computing models for networks have emerged, among which LOCAL, CONGEST, and Broadcast Congested Clique (BCC) play a prominent role. We consider hybrid models resulting from combining these three models. That is, we analyze the computing power of models allowing to, say, perform a constant number of rounds of CONGEST, then a constant number of rounds of LOCAL, then a constant number of rounds of BCC, possibly repeating this figure a constant number of times. We specifically focus on 2-round models, and we establish the complete picture of the relative powers of these models. That is, for every pair of such models, we determine whether one is (strictly) stronger than the other, or whether the two models are incomparable. The separation results are obtained by approaching communication complexity through an original angle, which may be of an independent interest. The two players are not bounded to compute the value of a binary function, but the combined outputs of the two players are constrained by this value. In particular, we introduce the XOR-Index problem, in which Alice is given a binary vector x ∈ {0,1}ⁿ together with an index i ∈ [n], Bob is given a binary vector y ∈ {0,1}ⁿ together with an index j ∈ [n], and, after a single round of 2-way communication, Alice must output a boolean out_A, and Bob must output a boolean out_B, such that out_A ∧ out_B = x_j⊕ y_i. We show that the communication complexity of XOR-Index is Ω(n) bits.
Cite as

Pierre Fraigniaud, Pedro Montealegre, Pablo Paredes, Ivan Rapaport, Martín Ríos-Wilson, and Ioan Todinca. Computing Power of Hybrid Models in Synchronous Networks. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 253, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fraigniaud_et_al:LIPIcs.OPODIS.2022.20,
  author =	{Fraigniaud, Pierre and Montealegre, Pedro and Paredes, Pablo and Rapaport, Ivan and R{\'\i}os-Wilson, Mart{\'\i}n and Todinca, Ioan},
  title =	{{Computing Power of Hybrid Models in Synchronous Networks}},
  booktitle =	{26th International Conference on Principles of Distributed Systems (OPODIS 2022)},
  pages =	{20:1--20:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-265-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{253},
  editor =	{Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2022.20},
  URN =		{urn:nbn:de:0030-drops-176401},
  doi =		{10.4230/LIPIcs.OPODIS.2022.20},
  annote =	{Keywords: hybrid model, synchronous networks, LOCAL, CONGEST, Broadcast Congested Clique}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2022.43
Brief Announcement: Computing Power of Hybrid Models in Synchronous Networks

Authors: Pierre Fraigniaud, Pedro Montealegre, Pablo Paredes, Ivan Rapaport, Martín Ríos-Wilson, and Ioan Todinca

Published in: LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)

Abstract
During the last two decades, a small set of distributed computing models for networks have emerged, among which LOCAL, CONGEST, and Broadcast Congested Clique (BCC) play a prominent role. We consider hybrid models resulting from combining these three models. That is, we analyze the computing power of models allowing to, say, perform a constant number of rounds of CONGEST, then a constant number of rounds of LOCAL, then a constant number of rounds of BCC, possibly repeating this figure a constant number of times. We specifically focus on 2-round models, and we establish the complete picture of the relative powers of these models. That is, for every pair of such models, we determine whether one is (strictly) stronger than the other, or whether the two models are incomparable.
Cite as

Pierre Fraigniaud, Pedro Montealegre, Pablo Paredes, Ivan Rapaport, Martín Ríos-Wilson, and Ioan Todinca. Brief Announcement: Computing Power of Hybrid Models in Synchronous Networks. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 43:1-43:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fraigniaud_et_al:LIPIcs.DISC.2022.43,
  author =	{Fraigniaud, Pierre and Montealegre, Pedro and Paredes, Pablo and Rapaport, Ivan and R{\'\i}os-Wilson, Mart{\'\i}n and Todinca, Ioan},
  title =	{{Brief Announcement: Computing Power of Hybrid Models in Synchronous Networks}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{43:1--43:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.43},
  URN =		{urn:nbn:de:0030-drops-172345},
  doi =		{10.4230/LIPIcs.DISC.2022.43},
  annote =	{Keywords: hybrid model, synchronous networks, LOCAL, CONGEST, Broadcast Congested Clique}
}
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