54 Search Results for "N�lis, Vincent"

Volume

LIPIcs, Volume 217

25th International Conference on Principles of Distributed Systems (OPODIS 2021)

OPODIS 2021, December 13-15, 2021, Strasbourg, France

Editors: Quentin Bramas, Vincent Gramoli, and Alessia Milani

Document
DOI: 10.4230/LIPIcs.CSL.2024.40
Syntactically and Semantically Regular Languages of λ-Terms Coincide Through Logical Relations

Authors: Vincent Moreau and Lê Thành Dũng (Tito) Nguyễn

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)

Abstract
A fundamental theme in automata theory is regular languages of words and trees, and their many equivalent definitions. Salvati has proposed a generalization to regular languages of simply typed λ-terms, defined using denotational semantics in finite sets. We provide here some evidence for its robustness. First, we give an equivalent syntactic characterization that naturally extends the seminal work of Hillebrand and Kanellakis connecting regular languages of words and syntactic λ-definability. Second, we show that any finitary extensional model of the simply typed λ-calculus, when used in Salvati’s definition, recognizes exactly the same class of languages of λ-terms as the category of finite sets does. The proofs of these two results rely on logical relations and can be seen as instances of a more general construction of a categorical nature, inspired by previous categorical accounts of logical relations using the gluing construction.
Cite as

Vincent Moreau and Lê Thành Dũng (Tito) Nguyễn. Syntactically and Semantically Regular Languages of λ-Terms Coincide Through Logical Relations. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 40:1-40:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{moreau_et_al:LIPIcs.CSL.2024.40,
  author =	{Moreau, Vincent and Nguy\~{ê}n, L\^{e} Th\`{a}nh D\~{u}ng (Tito)},
  title =	{{Syntactically and Semantically Regular Languages of \lambda-Terms Coincide Through Logical Relations}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{40:1--40:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.40},
  URN =		{urn:nbn:de:0030-drops-196831},
  doi =		{10.4230/LIPIcs.CSL.2024.40},
  annote =	{Keywords: regular languages, simple types, denotational semantics, logical relations}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2023.35
Atomic Register Abstractions for Byzantine-Prone Distributed Systems

Authors: Vincent Kowalski, Achour Mostéfaoui, and Matthieu Perrin

Published in: LIPIcs, Volume 286, 27th International Conference on Principles of Distributed Systems (OPODIS 2023)

Abstract
The construction of the atomic register abstraction over crash-prone asynchronous message-passing systems has been extensively studied since the founding work of Attiya, Bar-Noy, and Dolev. It has been shown that t < n/2 (where t is the maximal number of processes that may be faulty) is a necessary and sufficient requirement to build an atomic register. However, little attention has been paid to systems where faulty processes may exhibit a Byzantine behavior. This paper studies three definitions of linearizable single-writer multi-reader registers encountered in the state of the art: Read/Write registers whose read perations return the last written value, Read/Write-Increment registers whose read perations return both the last written value and the number of previously written values, and Read/Append registers whose read perations return the sequence of all previously written values. More specifically, it compares their computing power and the necessary and sufficient conditions on the maximum ratio t/n which makes it possible to build reductions from one register to another. Namely, we prove that t < n/3 is necessary and sufficient to implement a Read/Write-Increment register from Read/Write registers whereas this bound is only t < n/2 for a reduction from a Read/Append register to Read/Write-Increment registers. Reduction algorithms meeting these bounds are also provided.
Cite as

Vincent Kowalski, Achour Mostéfaoui, and Matthieu Perrin. Atomic Register Abstractions for Byzantine-Prone Distributed Systems. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 35:1-35:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kowalski_et_al:LIPIcs.OPODIS.2023.35,
  author =	{Kowalski, Vincent and Most\'{e}faoui, Achour and Perrin, Matthieu},
  title =	{{Atomic Register Abstractions for Byzantine-Prone Distributed Systems}},
  booktitle =	{27th International Conference on Principles of Distributed Systems (OPODIS 2023)},
  pages =	{35:1--35:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-308-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{286},
  editor =	{Bessani, Alysson and D\'{e}fago, Xavier and Nakamura, Junya and Wada, Koichi and Yamauchi, Yukiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2023.35},
  URN =		{urn:nbn:de:0030-drops-195257},
  doi =		{10.4230/LIPIcs.OPODIS.2023.35},
  annote =	{Keywords: Byzantine processes, Concurrent Object, Linearizability, Shared Register}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.1
On Complexity of 1-Center in Various Metrics

Authors: Amir Abboud, MohammadHossein Bateni, Vincent Cohen-Addad, Karthik C. S., and Saeed Seddighin

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
We consider the classic 1-center problem: Given a set P of n points in a metric space find the point in P that minimizes the maximum distance to the other points of P. We study the complexity of this problem in d-dimensional 𝓁_p-metrics and in edit and Ulam metrics over strings of length d. Our results for the 1-center problem may be classified based on d as follows. - Small d. Assuming the hitting set conjecture (HSC), we show that when d = ω(log n), no subquadratic algorithm can solve the 1-center problem in any of the 𝓁_p-metrics, or in the edit or Ulam metrics. - Large d. When d = Ω(n), we extend our conditional lower bound to rule out subquartic algorithms for the 1-center problem in edit metric (assuming Quantified SETH). On the other hand, we give a (1+ε)-approximation for 1-center in the Ulam metric with running time O_{ε}̃(nd+n²√d). We also strengthen some of the above lower bounds by allowing approximation algorithms or by reducing the dimension d, but only against a weaker class of algorithms which list all requisite solutions. Moreover, we extend one of our hardness results to rule out subquartic algorithms for the well-studied 1-median problem in the edit metric, where given a set of n strings each of length n, the goal is to find a string in the set that minimizes the sum of the edit distances to the rest of the strings in the set.
Cite as

Amir Abboud, MohammadHossein Bateni, Vincent Cohen-Addad, Karthik C. S., and Saeed Seddighin. On Complexity of 1-Center in Various Metrics. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 1:1-1:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{abboud_et_al:LIPIcs.APPROX/RANDOM.2023.1,
  author =	{Abboud, Amir and Bateni, MohammadHossein and Cohen-Addad, Vincent and Karthik C. S. and Seddighin, Saeed},
  title =	{{On Complexity of 1-Center in Various Metrics}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{1:1--1:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.1},
  URN =		{urn:nbn:de:0030-drops-188260},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.1},
  annote =	{Keywords: Center, Clustering, Edit metric, Ulam metric, Hamming metric, Fine-grained Complexity, Approximation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.16
Fully Polynomial-Time Algorithms Parameterized by Vertex Integrity Using Fast Matrix Multiplication

Authors: Matthias Bentert, Klaus Heeger, and Tomohiro Koana

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
We study the computational complexity of several polynomial-time-solvable graph problems parameterized by vertex integrity, a measure of a graph’s vulnerability to vertex removal in terms of connectivity. Vertex integrity is the smallest number ι such that there is a set S of ι' ≤ ι vertices such that every connected component of G-S contains at most ι-ι' vertices. It is known that the vertex integrity lies between the well-studied parameters vertex cover number and tree-depth. Our work follows similar studies for vertex cover number [Alon and Yuster, ESA 2007] and tree-depth [Iwata, Ogasawara, and Ohsaka, STACS 2018]. Alon and Yuster designed algorithms for graphs with small vertex cover number using fast matrix multiplications. We demonstrate that fast matrix multiplication can also be effectively used when parameterizing by vertex integrity ι by developing efficient algorithms for problems including an O(ι^{ω-1}n)-time algorithm for Maximum Matching and an O(ι^{(ω-1)/2}n²) ⊆ O(ι^{0.687} n²)-time algorithm for All-Pairs Shortest Paths. These algorithms can be faster than previous algorithms parameterized by tree-depth, for which fast matrix multiplication is not known to be effective.
Cite as

Matthias Bentert, Klaus Heeger, and Tomohiro Koana. Fully Polynomial-Time Algorithms Parameterized by Vertex Integrity Using Fast Matrix Multiplication. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 16:1-16:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bentert_et_al:LIPIcs.ESA.2023.16,
  author =	{Bentert, Matthias and Heeger, Klaus and Koana, Tomohiro},
  title =	{{Fully Polynomial-Time Algorithms Parameterized by Vertex Integrity Using Fast Matrix Multiplication}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{16:1--16:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.16},
  URN =		{urn:nbn:de:0030-drops-186692},
  doi =		{10.4230/LIPIcs.ESA.2023.16},
  annote =	{Keywords: FPT in P, Algebraic Algorithms, Adaptive Algorithms, Subgraph Detection, Matching, APSP}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.26
Algorithms for Length Spectra of Combinatorial Tori

Authors: Vincent Delecroix, Matthijs Ebbens, Francis Lazarus, and Ivan Yakovlev

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
Consider a weighted, undirected graph cellularly embedded on a topological surface. The function assigning to each free homotopy class of closed curves the length of a shortest cycle within this homotopy class is called the marked length spectrum. The (unmarked) length spectrum is obtained by just listing the length values of the marked length spectrum in increasing order. In this paper, we describe algorithms for computing the (un)marked length spectra of graphs embedded on the torus. More specifically, we preprocess a weighted graph of complexity n in time O(n² log log n) so that, given a cycle with 𝓁 edges representing a free homotopy class, the length of a shortest homotopic cycle can be computed in O(𝓁+log n) time. Moreover, given any positive integer k, the first k values of its unmarked length spectrum can be computed in time O(k log n). Our algorithms are based on a correspondence between weighted graphs on the torus and polyhedral norms. In particular, we give a weight independent bound on the complexity of the unit ball of such norms. As an immediate consequence we can decide if two embedded weighted graphs have the same marked spectrum in polynomial time. We also consider the problem of comparing the unmarked spectra and provide a polynomial time algorithm in the unweighted case and a randomized polynomial time algorithm otherwise.
Cite as

Vincent Delecroix, Matthijs Ebbens, Francis Lazarus, and Ivan Yakovlev. Algorithms for Length Spectra of Combinatorial Tori. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 26:1-26:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{delecroix_et_al:LIPIcs.SoCG.2023.26,
  author =	{Delecroix, Vincent and Ebbens, Matthijs and Lazarus, Francis and Yakovlev, Ivan},
  title =	{{Algorithms for Length Spectra of Combinatorial Tori}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{26:1--26:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.26},
  URN =		{urn:nbn:de:0030-drops-178765},
  doi =		{10.4230/LIPIcs.SoCG.2023.26},
  annote =	{Keywords: graphs on surfaces, length spectrum, polyhedral norm}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2023.62
Godzilla Onions: A Skit and Applet to Explain Euclidean Half-Plane Fractional Cascading (Media Exposition)

Authors: Richard Berger, Vincent Ha, David Kratz, Michael Lin, Jeremy Moyer, and Christopher J. Tralie

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
We provide a skit and an applet to illustrate fractional cascading in the context of half-plane range search for points in the Euclidean plane, which takes O(log N + h) output-sensitive time. In the video, a group of news anchors struggles to find the correct data structure to efficiently send out an early warning to the residents of Philadelphia who will be overtaken by a marching line of Godzillas. After exploring several options, the group eventually settles on onions and fractional cascading, only to discover that they themselves are in the line of fire! In the applet, we show step by step details of preprocessing to build the onions with fractional cascading and the subsequent query of the "Godzilla line" against the onion layers. Our video skit and applet can be found at https://ctralie.github.io/GodzillaOnions/
Cite as

Richard Berger, Vincent Ha, David Kratz, Michael Lin, Jeremy Moyer, and Christopher J. Tralie. Godzilla Onions: A Skit and Applet to Explain Euclidean Half-Plane Fractional Cascading (Media Exposition). In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 62:1-62:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{berger_et_al:LIPIcs.SoCG.2023.62,
  author =	{Berger, Richard and Ha, Vincent and Kratz, David and Lin, Michael and Moyer, Jeremy and Tralie, Christopher J.},
  title =	{{Godzilla Onions: A Skit and Applet to Explain Euclidean Half-Plane Fractional Cascading}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{62:1--62:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.62},
  URN =		{urn:nbn:de:0030-drops-179129},
  doi =		{10.4230/LIPIcs.SoCG.2023.62},
  annote =	{Keywords: convex hulls, onions, fractional cascading, visualization, d3}
}
Document
DOI: 10.4230/LIPIcs.DISC.2022.10
Holistic Verification of Blockchain Consensus

Authors: Nathalie Bertrand, Vincent Gramoli, Igor Konnov, Marijana Lazić, Pierre Tholoniat, and Josef Widder

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

Abstract
Blockchain has recently attracted the attention of the industry due, in part, to its ability to automate asset transfers. It requires distributed participants to reach a consensus on a block despite the presence of malicious (a.k.a. Byzantine) participants. Malicious participants exploit regularly weaknesses of these blockchain consensus algorithms, with sometimes devastating consequences. In fact, these weaknesses are quite common and are well illustrated by the flaws in various blockchain consensus algorithms [Pierre Tholoniat and Vincent Gramoli, 2019]. Paradoxically, until now, no blockchain consensus has been holistically verified. In this paper, we remedy this paradox by model checking for the first time a blockchain consensus used in industry. We propose a holistic approach to verify the consensus algorithm of the Red Belly Blockchain [Tyler Crain et al., 2021], for any number n of processes and any number f < n/3 of Byzantine processes. We decompose directly the algorithm pseudocode in two parts - an inner broadcast algorithm and an outer decision algorithm - each modelled as a threshold automaton [Igor Konnov et al., 2017], and we formalize their expected properties in linear-time temporal logic. We then automatically check the inner broadcasting algorithm, under a carefully identified fairness assumption. For the verification of the outer algorithm, we simplify the model of the inner algorithm by relying on its proven properties. Doing so, we formally verify, for any parameter, not only the safety properties of the Red Belly Blockchain consensus but also its liveness in less than 70 seconds.
Cite as

Nathalie Bertrand, Vincent Gramoli, Igor Konnov, Marijana Lazić, Pierre Tholoniat, and Josef Widder. Holistic Verification of Blockchain Consensus. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 10:1-10:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bertrand_et_al:LIPIcs.DISC.2022.10,
  author =	{Bertrand, Nathalie and Gramoli, Vincent and Konnov, Igor and Lazi\'{c}, Marijana and Tholoniat, Pierre and Widder, Josef},
  title =	{{Holistic Verification of Blockchain Consensus}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{10:1--10:24},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.10},
  URN =		{urn:nbn:de:0030-drops-172019},
  doi =		{10.4230/LIPIcs.DISC.2022.10},
  annote =	{Keywords: Model checking, automata, logic, byzantine failure}
}
Document
DOI: 10.4230/LIPIcs.DISC.2022.14
Byzantine Consensus Is Θ(n²): The Dolev-Reischuk Bound Is Tight Even in Partial Synchrony!

Authors: Pierre Civit, Muhammad Ayaz Dzulfikar, Seth Gilbert, Vincent Gramoli, Rachid Guerraoui, Jovan Komatovic, and Manuel Vidigueira

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

Abstract
The Dolev-Reischuk bound says that any deterministic Byzantine consensus protocol has (at least) quadratic communication complexity in the worst case. While it has been shown that the bound is tight in synchronous environments, it is still unknown whether a consensus protocol with quadratic communication complexity can be obtained in partial synchrony. Until now, the most efficient known solutions for Byzantine consensus in partially synchronous settings had cubic communication complexity (e.g., HotStuff, binary DBFT). This paper closes the existing gap by introducing SQuad, a partially synchronous Byzantine consensus protocol with quadratic worst-case communication complexity. In addition, SQuad is optimally-resilient and achieves linear worst-case latency complexity. The key technical contribution underlying SQuad lies in the way we solve view synchronization, the problem of bringing all correct processes to the same view with a correct leader for sufficiently long. Concretely, we present RareSync, a view synchronization protocol with quadratic communication complexity and linear latency complexity, which we utilize in order to obtain SQuad.
Cite as

Pierre Civit, Muhammad Ayaz Dzulfikar, Seth Gilbert, Vincent Gramoli, Rachid Guerraoui, Jovan Komatovic, and Manuel Vidigueira. Byzantine Consensus Is Θ(n²): The Dolev-Reischuk Bound Is Tight Even in Partial Synchrony!. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{civit_et_al:LIPIcs.DISC.2022.14,
  author =	{Civit, Pierre and Dzulfikar, Muhammad Ayaz and Gilbert, Seth and Gramoli, Vincent and Guerraoui, Rachid and Komatovic, Jovan and Vidigueira, Manuel},
  title =	{{Byzantine Consensus Is \Theta(n²): The Dolev-Reischuk Bound Is Tight Even in Partial Synchrony!}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{14:1--14:21},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.14},
  URN =		{urn:nbn:de:0030-drops-172059},
  doi =		{10.4230/LIPIcs.DISC.2022.14},
  annote =	{Keywords: Optimal Byzantine consensus, Communication complexity, Latency complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.7
Improved Approximation Algorithms and Lower Bounds for Search-Diversification Problems

Authors: Amir Abboud, Vincent Cohen-Addad, Euiwoong Lee, and Pasin Manurangsi

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
We study several questions related to diversifying search results. We give improved approximation algorithms in each of the following problems, together with some lower bounds. 1) We give a polynomial-time approximation scheme (PTAS) for a diversified search ranking problem [Nikhil Bansal et al., 2010] whose objective is to minimizes the discounted cumulative gain. Our PTAS runs in time n^{2^O(log(1/ε)/ε)} ⋅ m^O(1) where n denotes the number of elements in the databases and m denotes the number of constraints. Complementing this result, we show that no PTAS can run in time f(ε) ⋅ (nm)^{2^o(1/ε)} assuming Gap-ETH and therefore our running time is nearly tight. Both our upper and lower bounds answer open questions from [Nikhil Bansal et al., 2010]. 2) We next consider the Max-Sum Dispersion problem, whose objective is to select k out of n elements from a database that maximizes the dispersion, which is defined as the sum of the pairwise distances under a given metric. We give a quasipolynomial-time approximation scheme (QPTAS) for the problem which runs in time n^{O_ε(log n)}. This improves upon previously known polynomial-time algorithms with approximate ratios 0.5 [Refael Hassin et al., 1997; Allan Borodin et al., 2017]. Furthermore, we observe that reductions from previous work rule out approximation schemes that run in n^õ_ε(log n) time assuming ETH. 3) Finally, we consider a generalization of Max-Sum Dispersion called Max-Sum Diversification. In addition to the sum of pairwise distance, the objective also includes another function f. For monotone submodular function f, we give a quasipolynomial-time algorithm with approximation ratio arbitrarily close to (1-1/e). This improves upon the best polynomial-time algorithm which has approximation ratio 0.5 [Allan Borodin et al., 2017]. Furthermore, the (1-1/e) factor is also tight as achieving better-than-(1-1/e) approximation is NP-hard [Uriel Feige, 1998].
Cite as

Amir Abboud, Vincent Cohen-Addad, Euiwoong Lee, and Pasin Manurangsi. Improved Approximation Algorithms and Lower Bounds for Search-Diversification Problems. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{abboud_et_al:LIPIcs.ICALP.2022.7,
  author =	{Abboud, Amir and Cohen-Addad, Vincent and Lee, Euiwoong and Manurangsi, Pasin},
  title =	{{Improved Approximation Algorithms and Lower Bounds for Search-Diversification Problems}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.7},
  URN =		{urn:nbn:de:0030-drops-163481},
  doi =		{10.4230/LIPIcs.ICALP.2022.7},
  annote =	{Keywords: Approximation Algorithms, Complexity, Data Mining, Diversification}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.33
Polynomial Delay Algorithm for Minimal Chordal Completions

Authors: Caroline Brosse, Vincent Limouzy, and Arnaud Mary

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
Motivated by the problem of enumerating all tree decompositions of a graph, we consider in this article the problem of listing all the minimal chordal completions of a graph. In [Carmeli et al., 2020] (Pods 2017) Carmeli et al. proved that all minimal chordal completions or equivalently all proper tree decompositions of a graph can be listed in incremental polynomial time using exponential space. The total running time of their algorithm is quadratic in the number of solutions and the existence of an algorithm whose complexity depends only linearly on the number of solutions remained open. We close this question by providing a polynomial delay algorithm to solve this problem which, moreover, uses polynomial space. Our algorithm relies on Proximity Search, a framework recently introduced by Conte and Uno [Conte and Uno, 2019] (Stoc 2019) which has been shown powerful to obtain polynomial delay algorithms, but generally requires exponential space. In order to obtain a polynomial space algorithm for our problem, we introduce a new general method called canonical path reconstruction to design polynomial delay and polynomial space algorithms based on proximity search.
Cite as

Caroline Brosse, Vincent Limouzy, and Arnaud Mary. Polynomial Delay Algorithm for Minimal Chordal Completions. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 33:1-33:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{brosse_et_al:LIPIcs.ICALP.2022.33,
  author =	{Brosse, Caroline and Limouzy, Vincent and Mary, Arnaud},
  title =	{{Polynomial Delay Algorithm for Minimal Chordal Completions}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{33:1--33:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.33},
  URN =		{urn:nbn:de:0030-drops-163740},
  doi =		{10.4230/LIPIcs.ICALP.2022.33},
  annote =	{Keywords: Graph Algorithm, Algorithmic Enumeration, Minimal chordal completions}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.68
Galloping in Fast-Growth Natural Merge Sorts

Authors: Elahe Ghasemi, Vincent Jugé, and Ghazal Khalighinejad

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
We study the impact of sub-array merging routines on merge-based sorting algorithms. More precisely, we focus on the galloping sub-routine that TimSort uses to merge monotonic (non-decreasing) sub-arrays, hereafter called runs, and on the impact on the number of element comparisons performed if one uses this sub-routine instead of a naive merging routine. The efficiency of TimSort and of similar sorting algorithms has often been explained by using the notion of runs and the associated run-length entropy. Here, we focus on the related notion of dual runs, which was introduced in the 1990s, and the associated dual run-length entropy. We prove, for this complexity measure, results that are similar to those already known when considering standard run-induced measures: in particular, TimSort requires only 𝒪(n + n log(σ)) element comparisons to sort arrays of length n with σ distinct values. In order to do so, we introduce new notions of fast- and middle-growth for natural merge sorts (i.e., algorithms based on merging runs). By using these notions, we prove that several merge sorting algorithms, provided that they use TimSort’s galloping sub-routine for merging runs, are as efficient as TimSort at sorting arrays with low run-induced or dual-run-induced complexities.
Cite as

Elahe Ghasemi, Vincent Jugé, and Ghazal Khalighinejad. Galloping in Fast-Growth Natural Merge Sorts. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 68:1-68:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ghasemi_et_al:LIPIcs.ICALP.2022.68,
  author =	{Ghasemi, Elahe and Jug\'{e}, Vincent and Khalighinejad, Ghazal},
  title =	{{Galloping in Fast-Growth Natural Merge Sorts}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{68:1--68:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.68},
  URN =		{urn:nbn:de:0030-drops-164098},
  doi =		{10.4230/LIPIcs.ICALP.2022.68},
  annote =	{Keywords: Sorting algorithms, Merge sorting algorithms, Analysis of algorithms}
}
Document
DOI: 10.4230/LIPIcs.CPM.2022.8
Reduction Ratio of the IS-Algorithm: Worst and Random Cases

Authors: Vincent Jugé

Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)

Abstract
We study the IS-algorithm, a well-known linear-time algorithm for computing the suffix array of a word. This algorithm relies on transforming the input word w into another word, called the reduced word of w, that will be at least twice shorter; then, the algorithm recursively computes the suffix array of the reduced word. In this article, we study the reduction ratio of the IS-algorithm, i.e., the ratio between the lengths of the input word and the word obtained after reducing k times the input word. We investigate both worst cases, in which we find precise results, and random cases, where we prove some strong convergence phenomena. Finally, we prove that, if the input word is a randomly chosen word of length n, we should not expect much more than log(log(n)) recursive function calls.
Cite as

Vincent Jugé. Reduction Ratio of the IS-Algorithm: Worst and Random Cases. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 8:1-8:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{juge:LIPIcs.CPM.2022.8,
  author =	{Jug\'{e}, Vincent},
  title =	{{Reduction Ratio of the IS-Algorithm: Worst and Random Cases}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{8:1--8:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-234-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{223},
  editor =	{Bannai, Hideo and Holub, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.8},
  URN =		{urn:nbn:de:0030-drops-161357},
  doi =		{10.4230/LIPIcs.CPM.2022.8},
  annote =	{Keywords: Word combinatorics, Suffix array, IS algorithm}
}
Document
DOI: 10.4230/LIPIcs.CPM.2022.21
Permutation Pattern Matching for Doubly Partially Ordered Patterns

Authors: Laurent Bulteau, Guillaume Fertin, Vincent Jugé, and Stéphane Vialette

Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)

Abstract
We study in this paper the Doubly Partially Ordered Pattern Matching (or DPOP Matching) problem, a natural extension of the Permutation Pattern Matching problem. Permutation Pattern Matching takes as input two permutations σ and π, and asks whether there exists an occurrence of σ in π; whereas DPOP Matching takes two partial orders P_v and P_p defined on the same set X and a permutation π, and asks whether there exist |X| elements in π whose values (resp., positions) are in accordance with P_v (resp., P_p). Posets P_v and P_p aim at relaxing the conditions formerly imposed by the permutation σ, since σ yields a total order on both positions and values. Our problem being NP-hard in general (as Permutation Pattern Matching is), we consider restrictions on several parameters/properties of the input, e.g., bounding the size of the pattern, assuming symmetry of the posets (i.e., P_v and P_p are identical), assuming that one partial order is a total (resp., weak) order, bounding the length of the longest chain/anti-chain in the posets, or forbidding specific patterns in π. For each such restriction, we provide results which together give a(n almost) complete landscape for the algorithmic complexity of the problem.
Cite as

Laurent Bulteau, Guillaume Fertin, Vincent Jugé, and Stéphane Vialette. Permutation Pattern Matching for Doubly Partially Ordered Patterns. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bulteau_et_al:LIPIcs.CPM.2022.21,
  author =	{Bulteau, Laurent and Fertin, Guillaume and Jug\'{e}, Vincent and Vialette, St\'{e}phane},
  title =	{{Permutation Pattern Matching for Doubly Partially Ordered Patterns}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{21:1--21:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-234-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{223},
  editor =	{Bannai, Hideo and Holub, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.21},
  URN =		{urn:nbn:de:0030-drops-161481},
  doi =		{10.4230/LIPIcs.CPM.2022.21},
  annote =	{Keywords: Partial orders, Permutations, Pattern Matching, Algorithmic Complexity, Parameterized Complexity}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.SWAT.2022.3
Reconstructing the Tree of Life (Fitting Distances by Tree Metrics) (Invited Paper)

Authors: Mikkel Thorup

Published in: LIPIcs, Volume 227, 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)

Abstract
We consider the numerical taxonomy problem of fitting an S× S distance matrix D with a tree metric T. Here T is a weighted tree spanning S where the path lengths in T induce a metric on S. If there is a tree metric matching D exactly, then it is easily found. If there is no exact match, then for some k, we want to minimize the L_k norm of the errors, that is, pick T so as to minimize ‖D-T‖_k = (∑_{i,j ∈ S} |D(i,j)-T(i,j)|^k) ^{1/k}. This problem was raised in biology in the 1960s for k = 1,2. The biological interpretation is that T represents a possible evolution behind the species in S matching some measured distances in D. Sometimes, it is required that T is an ultrametric, meaning that all species are at the same distance from the root. An evolutionary tree induces a hierarchical classification of species and this is not just tied to biology. Medicine, ecology and linguistics are just some of the fields where this concept appears, and it is even an integral part of machine learning and data science. Fundamentally, if we can approximate distances with a tree, then they are much easier to reason about: many questions that are NP-hard for general metrics can be answered in linear time on tree metrics. In fact, humans have appreciated hierarchical classifications at least since Plato and Aristotle (350 BC). The numerical taxonomy problem is important in practice and many heuristics have been proposed. In this talk we will review the basic algorithmic theory, results and techniques, for the problem, including the most recent result from FOCS'21 [Vincent Cohen-Addad et al., 2021]. They paint a varied landscape with big differences between different moments, and with some very nice open problems remaining. - At STOC'93, Farach, Kannan, and Warnow [Martin Farach et al., 1995] proved that under L_∞, we can find the optimal ultrametric. Almost all other variants of the problem are APX-hard. - At SODA'96, Agarwala, Bafna, Farach, Paterson, and Thorup [Richa Agarwala et al., 1999] showed that for any norm L_k, k ≥ 1, if the best ultrametric can be α-approximated, then the best tree metric can be 3α-approximated. In particular, this implied a 3-approximation for tree metrics under L_∞. - At FOCS'05, Ailon and Charikar [Nir Ailon and Moses Charikar, 2011] showed that for any L_k, k ≥ 1, we can get an approximation factor of O(((log n)(log log n))^{1/k}) for both tree and ultrametrics. Their paper was focused on the L₁ norm, and they wrote "Determining whether an O(1) approximation can be obtained is a fascinating question". - At FOCS'21, Cohen-Addad, Das, Kipouridis, Parotsidis, and Thorup [Vincent Cohen-Addad et al., 2021] showed that indeed a constant factor is possible for L₁ for both tree and ultrametrics. This uses the special structure of L₁ in relation to hierarchies. - The status of L_k is wide open for 1 < k < ∞. All we know is that the approximation factor is between Ω(1) and O((log n)(log log n)).
Cite as

Mikkel Thorup. Reconstructing the Tree of Life (Fitting Distances by Tree Metrics) (Invited Paper). In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 3:1-3:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{thorup:LIPIcs.SWAT.2022.3,
  author =	{Thorup, Mikkel},
  title =	{{Reconstructing the Tree of Life (Fitting Distances by Tree Metrics)}},
  booktitle =	{18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)},
  pages =	{3:1--3:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-236-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{227},
  editor =	{Czumaj, Artur and Xin, Qin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.3},
  URN =		{urn:nbn:de:0030-drops-161631},
  doi =		{10.4230/LIPIcs.SWAT.2022.3},
  annote =	{Keywords: Numerical taxonomy, computational phylogenetics, hierarchical clustering}
}
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