DROPS

Volume

LIPIcs, Volume 292

3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)

SAND 2024, June 5-7, 2024, Patras, Greece

Editors: Arnaud Casteigts and Fabian Kuhn

Volume

LIPIcs, Volume 80

44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

ICALP 2017, July 10-14, 2017, Warsaw, Poland

Editors: Ioannis Chatzigiannakis, Piotr Indyk, Fabian Kuhn, and Anca Muscholl

Document

DOI: 10.4230/LIPIcs.STACS.2026.79

Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More

Authors: Mihail Stoian

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract

Despite much research, hard weighted problems still resist super-polynomial improvements over their textbook solution. On the other hand, the unweighted versions of these problems have recently witnessed the sought-after speedups. Currently, the only way to repurpose the algorithm of the unweighted version for the weighted version is to employ a polynomial embedding of the input weights. This, however, introduces a pseudo-polynomial factor into the running time, which becomes impractical for arbitrarily weighted instances. In this paper, we introduce a new way to repurpose the algorithm of the unweighted problem. Specifically, we show that the time complexity of several well-known NP-hard problems operating over the (min, +) and (max, +) semirings, such as TSP, Weighted Max-Cut, and Edge-Weighted k-Clique, is proportional to that of their unweighted versions when the set of input weights has small doubling. We achieve this by a meta-algorithm that converts the input weights into polynomially bounded integers using the recent constructive Freiman’s theorem by Randolph and Węgrzycki [ESA 2024] before applying the polynomial embedding.

Cite as

Mihail Stoian. Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 79:1-79:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{stoian:LIPIcs.STACS.2026.79,
  author =	{Stoian, Mihail},
  title =	{{Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{79:1--79:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.79},
  URN =		{urn:nbn:de:0030-drops-255680},
  doi =		{10.4230/LIPIcs.STACS.2026.79},
  annote =	{Keywords: doubling constant parametrization, weighted problems, traveling salesman, weighted max-cut, edge-weighted k-clique}
}

Document

DOI: 10.4230/LIPIcs.STACS.2026.71

Broadcast in Almost Mixing Time

Authors: Anton Paramonov and Roger Wattenhofer

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract

We study the problem of broadcasting multiple messages in the CONGEST model. In this problem, a dedicated source node s possesses a set M of messages with every message of size O(log n) where n is the total number of nodes. The objective is to ensure that every node in the network learns all messages in M. The execution of an algorithm progresses in rounds, and we focus on optimizing the round complexity of broadcasting multiple messages. Our primary contribution is a randomized algorithm for networks with expander topology. The algorithm succeeds with high probability and achieves a round complexity that is optimal up to a factor of the network’s mixing time and polylogarithmic terms. It leverages a multi-COBRA primitive, which uses multiple branching random walks running in parallel. A crucial aspect of our method is the use of these branching random walks to construct an optimal (up to a polylogarithmic factor) tree packing of a random graph, which is then used for efficient broadcasting. We also prove the problem to be NP-hard in a centralized setting and provide insights into why lower bounds that can be matched in expanders, namely graph diameter and |M|/minCut, cannot be tight in general graphs.

Cite as

Anton Paramonov and Roger Wattenhofer. Broadcast in Almost Mixing Time. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 71:1-71:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{paramonov_et_al:LIPIcs.STACS.2026.71,
  author =	{Paramonov, Anton and Wattenhofer, Roger},
  title =	{{Broadcast in Almost Mixing Time}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{71:1--71:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.71},
  URN =		{urn:nbn:de:0030-drops-255603},
  doi =		{10.4230/LIPIcs.STACS.2026.71},
  annote =	{Keywords: Distributed algorithms, Expander Graphs, Random graphs, Broadcast, Branching random walks, Tree packing, CONGEST model}
}

Document

DOI: 10.4230/LIPIcs.STACS.2026.4

Unit Interval Selection in Random Order Streams

Authors: Cezar-Mihail Alexandru, Adithya Diddapur, Magnús M. Halldórsson, Christian Konrad, and Kheeran K. Naidu

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract

We consider the Unit Interval Selection problem in the one-pass random order streaming model. In this setting, an algorithm is presented with a sequence of n unit-length intervals on the line that arrive in uniform random order, one at a time, and the objective is to output (an approximation of) a largest set of disjoint intervals using space linear in the size of an optimal solution. Previous work only considered adversarially ordered streams and established that, within these space constraints, a (2/3)-approximation can be achieved in such streams, and this is best possible, in that going beyond such an approximation factor requires space Ω(n) [Emek et al., TALG'16]. In this work, we show that an improved expected approximation factor can be achieved if the input stream is in uniform random order, where the expectation is taken over the stream order. More specifically, we give a one-pass streaming algorithm with expected approximation factor 0.7401 that uses space O(|OPT|), where OPT denotes an optimal solution. We also show that random order algorithms with expected approximation factor above 8/9 require space Ω(n), and algorithms that compute a better than 2/3-approximation with probability above 2/3 also require Ω(n) space. On a technical level, we design an algorithm for the restricted domain [0, Δ), for some constant Δ, and use standard techniques to obtain an algorithm for unrestricted domains. For the restricted domain [0, Δ), we run O(Δ) recursive instances of our algorithm, with each instance targeting the situation where a specific interval of an optimal solution arrives first. We establish the interesting property of our algorithm that it performs worst when the input stream consists solely of a set of independent intervals. It then remains to analyse the algorithm on these simple instances. Our lower bound is proved via communication complexity arguments, similar in spirit to the robust communication lower bounds established by [Chakrabarti et al., Theory Comput. 2016].

Cite as

Cezar-Mihail Alexandru, Adithya Diddapur, Magnús M. Halldórsson, Christian Konrad, and Kheeran K. Naidu. Unit Interval Selection in Random Order Streams. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{alexandru_et_al:LIPIcs.STACS.2026.4,
  author =	{Alexandru, Cezar-Mihail and Diddapur, Adithya and Halld\'{o}rsson, Magn\'{u}s M. and Konrad, Christian and Naidu, Kheeran K.},
  title =	{{Unit Interval Selection in Random Order Streams}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{4:1--4:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.4},
  URN =		{urn:nbn:de:0030-drops-254933},
  doi =		{10.4230/LIPIcs.STACS.2026.4},
  annote =	{Keywords: Random order streaming algorithms, unit interval selection}
}

Document

DOI: 10.4230/LIPIcs.CSL.2026.26

ε-Distance via Lévy-Prokhorov Lifting

Authors: Josée Desharnais and Ana Sokolova

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract

The most studied and accepted pseudometric for probabilistic processes is one based on the Kantorovich distance between distributions. It comes with many theoretical and motivating results, in particular it is the fixpoint of a given functional and defines a functor on (complete) pseudometric spaces. It is also the foundation for a categorical lifting of pseudometrics. Other notions of behavioural pseudometrics have also been proposed, one of them (ε-distance) based on ε-bisimulation. ε-Distance has the advantages that it is intuitively easy to understand, it relates systems that are conceptually close (for example, an imperfect implementation is close to its specification), and it comes equipped with a natural notion of ε-coupling. Finally, this distance is easy to compute. We show that ε-distance is also the greatest fixpoint of a functional and provides a functor. The latter is obtained by replacing the Kantorovich distance in the lifting functor with the Lévy-Prokhorov distance. In addition, we show that ε-couplings and ε-bisimulations have an appealing coalgebraic characterization.

Cite as

Josée Desharnais and Ana Sokolova. ε-Distance via Lévy-Prokhorov Lifting. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 26:1-26:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{desharnais_et_al:LIPIcs.CSL.2026.26,
  author =	{Desharnais, Jos\'{e}e and Sokolova, Ana},
  title =	{{\epsilon-Distance via L\'{e}vy-Prokhorov Lifting}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{26:1--26:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.26},
  URN =		{urn:nbn:de:0030-drops-254506},
  doi =		{10.4230/LIPIcs.CSL.2026.26},
  annote =	{Keywords: L\'{e}vy-Prokhorov metric, behavioural distance, epsilon-bisimulation, reactive probabilistic transition systems, discrete labelled Markov processes, coalgebraic epsilon-(bi)simulation}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.74

Adversarially-Robust Gossip Algorithms for Approximate Quantile and Mean Computations

Authors: Bernhard Haeupler, Marc Kaufmann, Raghu Raman Ravi, and Ulysse Schaller

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

Abstract

This paper presents gossip algorithms for aggregation tasks that demonstrate both robustness to adversarial corruptions of any order of magnitude and optimality across a substantial range of these corruption levels. Gossip algorithms distribute information in a scalable and efficient way by having random pairs of nodes exchange small messages. Value aggregation problems are of particular interest in this setting, as they occur frequently in practice, and many elegant algorithms have been proposed for computing aggregates and statistics such as averages and quantiles. An important and well-studied advantage of gossip algorithms is their robustness to message delays, network churn, and unreliable message transmissions. However, these crucial robustness guarantees only hold if all nodes follow the protocol and no messages are corrupted. In this paper, we remedy this by providing a framework to model both adversarial participants and message corruptions in gossip-style communications by allowing an adversary to control a small fraction of the nodes or corrupt messages arbitrarily. Despite this very powerful and general corruption model, we show that robust gossip algorithms can be designed for many important aggregation problems. Our algorithms guarantee that almost all nodes converge to an approximately correct answer with optimal efficiency and essentially as fast as without corruptions. The design of adversarially-robust gossip algorithms poses completely new challenges. Despite this, our algorithms remain very simple variations of known non-robust algorithms with often only subtle changes to avoid non-compliant nodes gaining too much influence over outcomes. While our algorithms remain simple, their analysis is much more complex and often requires a completely different approach than the non-adversarial setting.

Cite as

Bernhard Haeupler, Marc Kaufmann, Raghu Raman Ravi, and Ulysse Schaller. Adversarially-Robust Gossip Algorithms for Approximate Quantile and Mean Computations. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 74:1-74:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{haeupler_et_al:LIPIcs.ITCS.2026.74,
  author =	{Haeupler, Bernhard and Kaufmann, Marc and Ravi, Raghu Raman and Schaller, Ulysse},
  title =	{{Adversarially-Robust Gossip Algorithms for Approximate Quantile and Mean Computations}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{74:1--74:14},
  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.2026.74},
  URN =		{urn:nbn:de:0030-drops-253611},
  doi =		{10.4230/LIPIcs.ITCS.2026.74},
  annote =	{Keywords: Gossip Algorithms, Distributed Computing, Adversarial Robustness}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.75

Prior-Independent and Subgame Optimal Online Algorithms

Authors: Jason Hartline, Aleck Johnsen, and Anant Shah

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

Abstract

This paper develops two game-theoretic notions of beyond worst-case analysis that give better than worst-case guarantees on natural inputs. We illustrate them through the finite-horizon ski-rental problem. First, we consider prior-independent design and analysis of online algorithms where, rather than choosing a worst-case input, the adversary chooses a worst-case independent and identical distribution over inputs. Prior-independent online algorithms are generally analytically intractable; instead we give a fully polynomial-time approximation scheme to compute them. Second, we consider the worst-case design of algorithms. We define "subgame optimality" which is stronger than worst-case optimality in that it requires the algorithm to take advantage of an adversary not playing a worst-case input. Algorithms that focus only on the worst case can be far from subgame optimal. Highlighting the potential improvement from these paradigms for the finite-horizon ski-rental problem, we empirically compare worst-case, subgame optimal, and prior-independent algorithms in the prior-independent framework. Finally, we analyze the structure of their decisions across input sequences: the prior-independent algorithm exhibits more extreme adaptations to observed data, in contrast with the more conservative behavior of worst-case and subgame optimal algorithms.

Cite as

Jason Hartline, Aleck Johnsen, and Anant Shah. Prior-Independent and Subgame Optimal Online Algorithms. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 75:1-75:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hartline_et_al:LIPIcs.ITCS.2026.75,
  author =	{Hartline, Jason and Johnsen, Aleck and Shah, Anant},
  title =	{{Prior-Independent and Subgame Optimal Online Algorithms}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{75:1--75:23},
  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.2026.75},
  URN =		{urn:nbn:de:0030-drops-253622},
  doi =		{10.4230/LIPIcs.ITCS.2026.75},
  annote =	{Keywords: online algorithms, prior-independent algorithm design, zero-sum games}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.4

Pseudodeterministic Algorithms for Minimum Cut Problems

Authors: Aryan Agarwala and Nithin Varma

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

Abstract

In this paper we present efficient pseudodeterministic algorithms for both the global minimum cut and minimum s-t cut problems. The running time of our algorithm for the global minimum cut problem is asymptotically better than the fastest sequential deterministic global minimum cut algorithm (Henzinger, Li, Rao, Wang; SODA 2024). Furthermore, we implement our algorithm in streaming, PRAM, and cut-query models, where no efficient deterministic global minimum cut algorithms are known.

Cite as

Aryan Agarwala and Nithin Varma. Pseudodeterministic Algorithms for Minimum Cut Problems. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{agarwala_et_al:LIPIcs.ITCS.2026.4,
  author =	{Agarwala, Aryan and Varma, Nithin},
  title =	{{Pseudodeterministic Algorithms for Minimum Cut Problems}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{4:1--4:15},
  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.2026.4},
  URN =		{urn:nbn:de:0030-drops-252917},
  doi =		{10.4230/LIPIcs.ITCS.2026.4},
  annote =	{Keywords: Minimum Cut, Pseudodeterministic Algorithms}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.54

Testable Algorithms for Approximately Counting Edges and Triangles in Sublinear Time and Space

Authors: Talya Eden, Ronitt Rubinfeld, and Arsen Vasilyan

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

Abstract

We consider the fundamental problems of approximately counting the numbers of edges and triangles in a graph in sublinear time. Previous algorithms for these tasks are significantly more efficient under a promise that the arboricity of the graph is bounded by some parameter ̅α. However, when this promise is violated, the estimates given by these algorithms are no longer guaranteed to be correct. For the triangle counting task, we give an algorithm that requires no promise on the input graph G, and computes a (1±ε)-approximation for the number of triangles t in G in time O^*((m⋅ α(G))/t + m/(t^{2/3)}), where α(G) is the arboricity of the graph. The algorithm can be used on any graph G (no prior knowledge of the arboricity α(G) is required), and the algorithm adapts its run-time on the fly based on the graph G. We accomplish this by trying a sequence of candidate values α̃ for α(G) and using a novel algorithm in the framework of testable algorithms. This ensures that wrong candidates α̃ cannot lead to wrong estimates: if the advice is incorrect, the algorithm either succeeds despite this or detects this and continues with a new candidate. Once the algorithm accepts the candidate, its output is guaranteed to be correct with high probability. We prove that this approach preserves - up to an additive overhead - the dramatic efficiency gains obtainable when good arboricity bounds are known in advance, while ensuring robustness against misleading advice. We further complement this result with a lower bound, showing that such an overhead is unavoidable whenever the advice may be faulty. We further demonstrate implications of our results for triangle counting in the streaming model.

Cite as

Talya Eden, Ronitt Rubinfeld, and Arsen Vasilyan. Testable Algorithms for Approximately Counting Edges and Triangles in Sublinear Time and Space. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 54:1-54:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{eden_et_al:LIPIcs.ITCS.2026.54,
  author =	{Eden, Talya and Rubinfeld, Ronitt and Vasilyan, Arsen},
  title =	{{Testable Algorithms for Approximately Counting Edges and Triangles in Sublinear Time and Space}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{54:1--54:24},
  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.2026.54},
  URN =		{urn:nbn:de:0030-drops-253417},
  doi =		{10.4230/LIPIcs.ITCS.2026.54},
  annote =	{Keywords: Sublinear Algorithms, Triangle Counting, Edge Counting, Arboricity}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.63

Perfect Simulation of Las Vegas Algorithms via Local Computation

Authors: Xinyu Fu, Yonggang Jiang, and Yitong Yin

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

Abstract

The notion of Las Vegas algorithms was introduced by Babai (1979) and can be defined in two ways: - In Babai’s original definition, a randomized algorithm is called Las Vegas if it has a finitely bounded running time and certifiable random failure. - Another definition widely accepted today is that Las Vegas algorithms refer to zero-error randomized algorithms with random running times. The equivalence between the two definitions is straightforward. Specifically, for randomized algorithms with certifiable failures, repeatedly running the algorithm until no failure is encountered allows for faithful simulation of the correct output when it executes successfully. We show that a similar perfect simulation can also be achieved in distributed local computation. Specifically, in the LOCAL model, with a polylogarithmic overhead in time complexity, any Las Vegas algorithm with finitely bounded running time and locally certifiable failures can be converted to a zero error Las Vegas algorithm. This transformed algorithm faithfully reproduces the correct output of the original algorithm in successful executions. This is achieved by a reduction to a distributed sampling problem under the Lovász Local Lemma (LLL), where the objective is to sample from the joint distribution of random variables avoiding all bad events. We then design the first efficient algorithm to solve this sampling problem in the LOCAL model.

Cite as

Xinyu Fu, Yonggang Jiang, and Yitong Yin. Perfect Simulation of Las Vegas Algorithms via Local Computation. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 63:1-63:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fu_et_al:LIPIcs.ITCS.2026.63,
  author =	{Fu, Xinyu and Jiang, Yonggang and Yin, Yitong},
  title =	{{Perfect Simulation of Las Vegas Algorithms via Local Computation}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{63:1--63:22},
  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.2026.63},
  URN =		{urn:nbn:de:0030-drops-253503},
  doi =		{10.4230/LIPIcs.ITCS.2026.63},
  annote =	{Keywords: Las Vegas algorithms, perfect simulation, Lov\'{a}sz Local Lemma, sampling}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.67

Query Lower Bounds for Correlation Clustering Under Memory Constraints

Authors: Sumegha Garg, Songhua He, and Periklis A. Papakonstantinou

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

Abstract

This work initiates the study of memory–query tradeoffs for graph problems, with a focus on correlation clustering. Correlation clustering asks for a partition of the vertices that minimizes disagreements: non‑edges inside clusters plus edges across clusters. Our first result is a tight query lower bound: to output a partition whose cost approximates the optimum up to an additive error of ε n², any algorithm requires Ω(n/ε²) adjacency-matrix queries. Under memory constraints, we show that even for the seemingly easier task of approximating the optimal clustering cost (without producing a partition), any algorithm in the random query model must make ≫ n/ε² adjacency-matrix queries. Finally, we prove the first general graph model query lower bound for correlation clustering, where algorithms are allowed adjacency-matrix, neighbor, and degree queries. The latter two bounds are not yet tight, leaving room for sharper results.

Cite as

Sumegha Garg, Songhua He, and Periklis A. Papakonstantinou. Query Lower Bounds for Correlation Clustering Under Memory Constraints. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 67:1-67:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{garg_et_al:LIPIcs.ITCS.2026.67,
  author =	{Garg, Sumegha and He, Songhua and Papakonstantinou, Periklis A.},
  title =	{{Query Lower Bounds for Correlation Clustering Under Memory Constraints}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{67:1--67:24},
  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.2026.67},
  URN =		{urn:nbn:de:0030-drops-253542},
  doi =		{10.4230/LIPIcs.ITCS.2026.67},
  annote =	{Keywords: correlation clustering, query-space complexity, information theory}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.36

Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election

Authors: Yi-Jun Chang, Lyuting Chen, and Haoran Zhou

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

Abstract

The content-oblivious model, introduced by Censor-Hillel, Cohen, Gelles, and Sela (PODC 2022; Distributed Computing 2023), captures an extremely weak form of communication where nodes can only send asynchronous, content-less pulses. They showed that in 2-edge-connected networks, any distributed algorithm can be simulated in the content-oblivious model, provided that a unique leader is designated a priori. Subsequent works of Frei, Gelles, Ghazy, and Nolin (DISC 2024) and Chalopin et al. (DISC 2025) developed content-oblivious leader election algorithms, first for unoriented rings and then for general 2-edge-connected graphs. These results establish that all graph problems are solvable in content-oblivious, 2-edge-connected networks. Much less is known about networks that are not 2-edge-connected. Censor-Hillel, Cohen, Gelles, and Sela showed that no non-constant function f(x,y) can be computed correctly by two parties using content-oblivious communication over a single edge, where one party holds x and the other holds y. This seemingly ruled out many natural graph problems on non-2-edge-connected graphs. In this work, we show that, with the knowledge of network topology G, leader election is possible in a wide range of graphs. Our main contributions are as follows: Impossibility: Graphs symmetric about an edge admit no randomized terminating leader election algorithm, even when nodes have unique identifiers and full knowledge of G. Leader election algorithms: Trees that are not symmetric about any edge admit a quiescently terminating leader election algorithm with topology knowledge, even in anonymous networks, using O(n²) messages, where n is the number of nodes. Moreover, even-diameter trees admit a terminating leader election given only the knowledge of the network diameter D = 2r, with message complexity O(nr). Necessity of topology knowledge: In the family of graphs 𝒢 = {P₃, P₅}, both the 3-path P₃ and the 5-path P₅ admit a quiescently terminating leader election if nodes know the topology exactly. However, if nodes only know that the underlying topology belongs to 𝒢, then terminating leader election is impossible.

Cite as

Yi-Jun Chang, Lyuting Chen, and Haoran Zhou. Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 36:1-36:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chang_et_al:LIPIcs.ITCS.2026.36,
  author =	{Chang, Yi-Jun and Chen, Lyuting and Zhou, Haoran},
  title =	{{Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{36:1--36:23},
  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.2026.36},
  URN =		{urn:nbn:de:0030-drops-253239},
  doi =		{10.4230/LIPIcs.ITCS.2026.36},
  annote =	{Keywords: Asynchronous model, fault tolerance, quiescent termination}
}

Document

DOI: 10.4230/LIPIcs.OPODIS.2025.10

Computing in a Faulty Congested Clique

Authors: Keren Censor-Hillel and Pedro Soto

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

Abstract

We study a Faulty Congested Clique model, in which an adversary may fail nodes in the network throughout the computation. We show that any task of O(nlog{n})-bit input per node can be solved in roughly n rounds, where n is the size of the network. This nearly matches the linear upper bound on the complexity of the non-faulty Congested Clique model for such problems, by learning the entire input, and it holds in the faulty model even with a linear number of faults. Our main contribution is that we establish that one can do much better by looking more closely at the computation. Given a deterministic algorithm 𝒜 for the non-faulty Congested Clique model, we show how to transform it into an algorithm 𝒜' for the faulty model, with an overhead that could be as small as some logarithmic-in-n factor, by considering refined complexity measures of 𝒜. As an exemplifying application of our approach, we show that the O(n^{1/3})-round complexity of semi-ring matrix multiplication [Censor{-}Hillel, Kaski, Korhonen, Lenzen, Paz, Suomela, PODC 2015] remains the same up to polylog factors in the faulty model, even if the adversary can fail 99% of the nodes (or any other constant fraction).

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Keren Censor-Hillel and Pedro Soto. Computing in a Faulty Congested Clique. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{censorhillel_et_al:LIPIcs.OPODIS.2025.10,
  author =	{Censor-Hillel, Keren and Soto, Pedro},
  title =	{{Computing in a Faulty Congested Clique}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{10:1--10:19},
  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.2025.10},
  URN =		{urn:nbn:de:0030-drops-251833},
  doi =		{10.4230/LIPIcs.OPODIS.2025.10},
  annote =	{Keywords: distributed computing, graph algorithms, computing with faults}
}

Document

DOI: 10.4230/LIPIcs.OPODIS.2025.15

Time-Optimal and Energy-Efficient Deterministic Consensus

Authors: Shachar Meir, Hugo Mirault, David Peleg, and Peter Robinson

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

Abstract

We study fault-tolerant consensus in a variant of the synchronous message passing model, where, in each round, every node can choose to be awake or asleep. This is known as the sleeping model (Chatterjee, Gmyr, Pandurangan PODC 2020) and defines the awake complexity (also called energy complexity), which measures the maximum number of rounds that any node is awake throughout the execution. Only awake nodes can send and receive messages in a given round and all messages sent to sleeping nodes are lost. We present new deterministic consensus algorithms that tolerate up to f < n crash failures, where n is the number of nodes. Our algorithms match the optimal time complexity lower bound of f+1 rounds. For multi-value consensus, where the input values are chosen from some possibly large set, we achieve an energy complexity of 𝒪(⌈ f² / n ⌉) rounds, whereas for binary consensus, we show an algorithm to achieve 𝒪(⌈ f / √n ⌉) energy complexity.

Cite as

Shachar Meir, Hugo Mirault, David Peleg, and Peter Robinson. Time-Optimal and Energy-Efficient Deterministic Consensus. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{meir_et_al:LIPIcs.OPODIS.2025.15,
  author =	{Meir, Shachar and Mirault, Hugo and Peleg, David and Robinson, Peter},
  title =	{{Time-Optimal and Energy-Efficient Deterministic Consensus}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{15:1--15:16},
  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.2025.15},
  URN =		{urn:nbn:de:0030-drops-251881},
  doi =		{10.4230/LIPIcs.OPODIS.2025.15},
  annote =	{Keywords: Distributed computing, Crash faults, Consensus, Energy complexity, Sleeping model}
}

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