12 Search Results for "Rabie, Mikaël"

Document
DOI: 10.4230/LIPIcs.DISC.2024.5
Asynchronous Fault-Tolerant Distributed Proper Coloring of Graphs

Authors: Alkida Balliu, Pierre Fraigniaud, Patrick Lambein-Monette, Dennis Olivetti, and Mikaël Rabie

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

Abstract
We revisit asynchronous computing in networks of crash-prone processes, under the asynchronous variant of the standard LOCAL model, recently introduced by Fraigniaud et al. [DISC 2022]. We focus on the vertex coloring problem, and our contributions concern both lower and upper bounds for this problem. On the upper bound side, we design an algorithm tolerating an arbitrarily large number of crash failures that computes an O(Δ²)-coloring of any n-node graph of maximum degree Δ, in O(log^⋆ n) rounds. This extends Linial’s seminal result from the (synchronous failure-free) LOCAL model to its asynchronous crash-prone variant. Then, by allowing a dependency on Δ on the runtime, we show that we can reduce the colors to ((1/2)(Δ+1)(Δ+2)-1). For cycles (i.e., for Δ = 2), our algorithm achieves a 5-coloring of any n-node cycle, in O(log^⋆ n) rounds. This improves the known 6-coloring algorithm by Fraigniaud et al., and fixes a bug in their algorithm, which was erroneously claimed to produce a 5-coloring. On the lower bound side, we show that, for k < 5, and for every prime integer n, no algorithm can k-color the n-node cycle in the asynchronous crash-prone variant of LOCAL, independently from the round-complexities of the algorithms. This lower bound is obtained by reduction from an original extension of the impossibility of solving weak symmetry-breaking in the wait-free shared-memory model. We show that this impossibility still holds even if the processes are provided with inputs susceptible to help breaking symmetry.
Cite as

Alkida Balliu, Pierre Fraigniaud, Patrick Lambein-Monette, Dennis Olivetti, and Mikaël Rabie. Asynchronous Fault-Tolerant Distributed Proper Coloring of Graphs. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{balliu_et_al:LIPIcs.DISC.2024.5,
  author =	{Balliu, Alkida and Fraigniaud, Pierre and Lambein-Monette, Patrick and Olivetti, Dennis and Rabie, Mika\"{e}l},
  title =	{{Asynchronous Fault-Tolerant Distributed Proper Coloring of Graphs}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{5:1--5:20},
  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.2024.5},
  URN =		{urn:nbn:de:0030-drops-212328},
  doi =		{10.4230/LIPIcs.DISC.2024.5},
  annote =	{Keywords: LOCAL model, Graph Coloring, Renaming, Weak Symmetry-Breaking, Fault-Tolerance, Wait-Free Computing}
}
Document
DOI: 10.4230/LIPIcs.DISC.2024.28
Self-Stabilizing MIS Computation in the Beeping Model

Authors: George Giakkoupis, Volker Turau, and Isabella Ziccardi

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

Abstract
We consider self-stabilizing algorithms to compute a Maximal Independent Set (MIS) in the extremely weak beeping communication model. The model consists of an anonymous network with synchronous rounds. In each round, each vertex can optionally transmit a signal to all its neighbors (beep). After the transmission of a signal, each vertex can only differentiate between no signal received, or at least one signal received. We also consider an extension of this model where vertices can transmit signals through two distinguishable beeping channels. We assume that vertices have some knowledge about the topology of the network. We revisit the not self-stabilizing algorithm proposed by Jeavons, Scott, and Xu (2013), which computes an MIS in the beeping model. We enhance this algorithm to be self-stabilizing, and explore three different variants, which differ in the knowledge about the topology available to the vertices and the number of beeping channels. In the first variant, every vertex knows an upper bound on the maximum degree Δ of the graph. For this case, we prove that the proposed self-stabilizing version maintains the same run-time as the original algorithm, i.e., it stabilizes after O(log n) rounds w.h.p. on any n-vertex graph. In the second variant, each vertex only knows an upper bound on its own degree. For this case, we prove that the algorithm stabilizes after O(log n⋅ log log n) rounds on any n-vertex graph, w.h.p. In the third variant, we consider the model with two beeping channels, where every vertex knows an upper bound of the maximum degree of the nodes in the 1-hop neighborhood. We prove that this variant stabilizes w.h.p. after O(log n) rounds.
Cite as

George Giakkoupis, Volker Turau, and Isabella Ziccardi. Self-Stabilizing MIS Computation in the Beeping Model. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 28:1-28:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{giakkoupis_et_al:LIPIcs.DISC.2024.28,
  author =	{Giakkoupis, George and Turau, Volker and Ziccardi, Isabella},
  title =	{{Self-Stabilizing MIS Computation in the Beeping Model}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{28:1--28:21},
  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.2024.28},
  URN =		{urn:nbn:de:0030-drops-212540},
  doi =		{10.4230/LIPIcs.DISC.2024.28},
  annote =	{Keywords: Maximal Independent Set, Self-Stabilization, Beeping Model}
}
Document
DOI: 10.4230/LIPIcs.DISC.2024.29
Massively Parallel Ruling Set Made Deterministic

Authors: Jeff Giliberti and Zahra Parsaeian

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

Abstract
We study the deterministic complexity of the 2-Ruling Set problem in the model of Massively Parallel Computation (MPC) with linear and strongly sublinear local memory. - Linear MPC: We present a constant-round deterministic algorithm for the 2-Ruling Set problem that matches the randomized round complexity recently settled by Cambus, Kuhn, Pai, and Uitto [DISC'23], and improves upon the deterministic O(log log n)-round algorithm by Pai and Pemmaraju [PODC'22]. Our main ingredient is a simpler analysis of CKPU’s algorithm based solely on bounded independence, which makes its efficient derandomization possible. - Sublinear MPC: We present a deterministic algorithm that computes a 2-Ruling Set in Õ(√{log n}) rounds deterministically. Notably, this is the first deterministic ruling set algorithm with sublogarithmic round complexity, improving on the O(log Δ + log log^* n)-round complexity that stems from the deterministic MIS algorithm of Czumaj, Davies, and Parter [TALG'21]. Our result is based on a simple and fast randomness-efficient construction that achieves the same sparsification as that of the randomized Õ(√{log n})-round LOCAL algorithm by Kothapalli and Pemmaraju [FSTTCS'12].
Cite as

Jeff Giliberti and Zahra Parsaeian. Massively Parallel Ruling Set Made Deterministic. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 29:1-29:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{giliberti_et_al:LIPIcs.DISC.2024.29,
  author =	{Giliberti, Jeff and Parsaeian, Zahra},
  title =	{{Massively Parallel Ruling Set Made Deterministic}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{29:1--29:21},
  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.2024.29},
  URN =		{urn:nbn:de:0030-drops-212551},
  doi =		{10.4230/LIPIcs.DISC.2024.29},
  annote =	{Keywords: deterministic algorithms, distributed computing, massively parallel computation, graph algorithms, derandomization}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2024.44
Brief Announcement: The Expressive Power of Uniform Population Protocols with Logarithmic Space

Authors: Philipp Czerner, Vincent Fischer, and Roland Guttenberg

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

Abstract
Population protocols are a model of computation in which indistinguishable mobile agents interact in pairs to decide a property of their initial configuration. Originally introduced by Angluin et. al. in 2004 with a constant number of states, research nowadays focuses on protocols where the space usage depends on the number of agents. The expressive power of population protocols has so far however only been determined for protocols using o(log n) states, which compute only semilinear predicates, and for Ω(n) states. This leaves a significant gap, particularly concerning protocols with Θ(log n) or Θ(polylog n) states, which are the most common constructions in the literature. In this paper we close the gap and prove that for any ε > 0 and f ∈ Ω(log n) ∩ 𝒪(n^{1-ε}), both uniform and non-uniform population protocols with Θ(f(n)) states can decide exactly NSPACE(f(n) log n).
Cite as

Philipp Czerner, Vincent Fischer, and Roland Guttenberg. Brief Announcement: The Expressive Power of Uniform Population Protocols with Logarithmic Space. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 44:1-44:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{czerner_et_al:LIPIcs.DISC.2024.44,
  author =	{Czerner, Philipp and Fischer, Vincent and Guttenberg, Roland},
  title =	{{Brief Announcement: The Expressive Power of Uniform Population Protocols with Logarithmic Space}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{44:1--44:7},
  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.2024.44},
  URN =		{urn:nbn:de:0030-drops-212726},
  doi =		{10.4230/LIPIcs.DISC.2024.44},
  annote =	{Keywords: Population Protocols, Uniform, Expressive Power}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2024.47
Brief Announcement: Agreement Tasks in Fault-Prone Synchronous Networks of Arbitrary Structures

Authors: Pierre Fraigniaud, Minh Hang Nguyen, and Ami Paz

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

Abstract
Consensus is arguably the most studied problem in distributed computing as a whole, and particularly in distributed message-passing settings. Research on consensus has considered various failure types, memory constraints, and much more. Surprisingly, almost all of this work assumes that messages are passed in a complete network, i.e., each process has a direct link to every other process. Set agreement, a relaxed variant of consensus, has also been heavily studied in different settings, yet research on it has also been limited to complete networks. We address this situation by considering consensus and set agreement in general networks, i.e., that can have an arbitrary graph G as their communication graph. We focus on fault-prone networks, where up to t nodes may crash and irrevocably stop communicating, and present upper and lower bounds for such networks. We establish the following collection of results: - The consensus algorithm by [Castañeda et al., 2023] is optimal for all graphs, and not only for symmetric graphs. - This algorithm can be extended to a generic algorithm for k-set agreement, for every k ≥ 1. For k = 1, our generic algorithm coincides with the existing one for consensus. - All these algorithms can be extended to the case where the number t of failures exceeds the connectivity κ of the graph, while the existing consensus algorithm assumed that t < κ.
Cite as

Pierre Fraigniaud, Minh Hang Nguyen, and Ami Paz. Brief Announcement: Agreement Tasks in Fault-Prone Synchronous Networks of Arbitrary Structures. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 47:1-47:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fraigniaud_et_al:LIPIcs.DISC.2024.47,
  author =	{Fraigniaud, Pierre and Nguyen, Minh Hang and Paz, Ami},
  title =	{{Brief Announcement: Agreement Tasks in Fault-Prone Synchronous Networks of Arbitrary Structures}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{47:1--47:5},
  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.2024.47},
  URN =		{urn:nbn:de:0030-drops-212755},
  doi =		{10.4230/LIPIcs.DISC.2024.47},
  annote =	{Keywords: Consensus, set-agreement, fault tolerance, crash failures}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.94
A Row Generation Algorithm for Finding Optimal Burning Sequences of Large Graphs

Authors: Felipe de Carvalho Pereira, Pedro Jussieu de Rezende, Tallys Yunes, and Luiz Fernando Batista Morato

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We propose an exact algorithm for the Graph Burning Problem (GBP), an NP-hard optimization problem that models the spread of influence on social networks. Given a graph G with vertex set V, the objective is to find a sequence of k vertices in V, namely, v₁, v₂, … , v_k, such that k is minimum and ⋃_{i=1}^{k} {u∈V: d(u,v_i) ≤ k-i} = V, where d(u,v) denotes the distance between u and v. We formulate the problem as a set covering integer programming model and design a row generation algorithm for the GBP. Our method exploits the fact that a very small number of covering constraints is often sufficient for solving the integer model, allowing the corresponding rows to be generated on demand. To date, the most efficient exact algorithm for the GBP, denoted here by GDCA, is able to obtain optimal solutions for graphs with up to 14,000 vertices within two hours of execution. In comparison, our algorithm finds provably optimal solutions approximately 236 times faster, on average, than GDCA. For larger graphs, memory space becomes a limiting factor for GDCA. Our algorithm, however, solves real-world instances with more than 3 million vertices in less than 19 minutes, increasing the size of graphs for which optimal solutions are known by a factor of 200. Additionally, we conduct tests on the proposed algorithm using a series of challenging instances composed of grid graphs containing up to 5,000 vertices. As a result, we achieve novel optimal solutions and tight optimality gaps that have not been previously reported in the literature.
Cite as

Felipe de Carvalho Pereira, Pedro Jussieu de Rezende, Tallys Yunes, and Luiz Fernando Batista Morato. A Row Generation Algorithm for Finding Optimal Burning Sequences of Large Graphs. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 94:1-94:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{pereira_et_al:LIPIcs.ESA.2024.94,
  author =	{Pereira, Felipe de Carvalho and de Rezende, Pedro Jussieu and Yunes, Tallys and Morato, Luiz Fernando Batista},
  title =	{{A Row Generation Algorithm for Finding Optimal Burning Sequences of Large Graphs}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{94:1--94:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.94},
  URN =		{urn:nbn:de:0030-drops-211651},
  doi =		{10.4230/LIPIcs.ESA.2024.94},
  annote =	{Keywords: Graph Burning, Burning Number, Burning Sequence, Set Covering, Integer Programming, Row Generation}
}
Document
DOI: 10.4230/LIPIcs.SAND.2023.7
When Should You Wait Before Updating? - Toward a Robustness Refinement

Authors: Swan Dubois, Laurent Feuilloley, Franck Petit, and Mikaël Rabie

Published in: LIPIcs, Volume 257, 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)

Abstract
Consider a dynamic network and a given distributed problem. At any point in time, there might exist several solutions that are equally good with respect to the problem specification, but that are different from an algorithmic perspective, because some could be easier to update than others when the network changes. In other words, one would prefer to have a solution that is more robust to topological changes in the network; and in this direction the best scenario would be that the solution remains correct despite the dynamic of the network. In [Arnaud Casteigts et al., 2020], the authors introduced a very strong robustness criterion: they required that for any removal of edges that maintain the network connected, the solution remains valid. They focus on the maximal independent set problem, and their approach consists in characterizing the graphs in which there exists a robust solution (the existential problem), or even stronger, where any solution is robust (the universal problem). As the robustness criteria is very demanding, few graphs have a robust solution, and even fewer are such that all of their solutions are robust. In this paper, we ask the following question: Can we have robustness for a larger class of networks, if we bound the number k of edge removals allowed? To answer this question, we consider three classic problems: maximal independent set, minimal dominating set and maximal matching. For the universal problem, the answers for the three cases are surprisingly different. For minimal dominating set, the class does not depend on the number of edges removed. For maximal matching, removing only one edge defines a robust class related to perfect matchings, but for all other bounds k, the class is the same as for an arbitrary number of edge removals. Finally, for maximal independent set, there is a strict hierarchy of classes: the class for the bound k is strictly larger than the class for bound k+1. For the robustness notion of [Arnaud Casteigts et al., 2020], no characterization of the class for the existential problem is known, only a polynomial-time recognition algorithm. We show that the situation is even worse for bounded k: even for k = 1, it is NP-hard to decide whether a graph has a robust maximal independent set.
Cite as

Swan Dubois, Laurent Feuilloley, Franck Petit, and Mikaël Rabie. When Should You Wait Before Updating? - Toward a Robustness Refinement. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dubois_et_al:LIPIcs.SAND.2023.7,
  author =	{Dubois, Swan and Feuilloley, Laurent and Petit, Franck and Rabie, Mika\"{e}l},
  title =	{{When Should You Wait Before Updating? - Toward a Robustness Refinement}},
  booktitle =	{2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-275-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{257},
  editor =	{Doty, David and Spirakis, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2023.7},
  URN =		{urn:nbn:de:0030-drops-179435},
  doi =		{10.4230/LIPIcs.SAND.2023.7},
  annote =	{Keywords: Robustness, dynamic network, temporal graphs, edge removal, connectivity, footprint, packing/covering problems, maximal independent set, maximal matching, minimum dominating set, perfect matching, NP-hardness}
}
Document
DOI: 10.4230/LIPIcs.SAND.2023.11
Making Self-Stabilizing Algorithms for Any Locally Greedy Problem

Authors: Johanne Cohen, Laurence Pilard, Mikaël Rabie, and Jonas Sénizergues

Published in: LIPIcs, Volume 257, 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)

Abstract
Self-stabilizing algorithms are a way to deal with network dynamicity, as it will update itself after a network change (addition or removal of nodes or edges), as long as changes are not frequent. We propose an automatic transformation of synchronous distributed algorithms that solve locally greedy and mendable problems into self-stabilizing algorithms in anonymous networks. Mendable problems are a generalization of greedy problems where any partial solution may be transformed -instead of completed- into a global solution: every time we extend the partial solution, we are allowed to change the previous partial solution up to a given distance. Locally here means that to extend a solution for a node, we need to look at a constant distance from it. In order to do this, we propose the first explicit self-stabilizing algorithm computing a (k,k-1)-ruling set (i.e. a "maximal independent set at distance k"). By combining this technique multiple times, we compute a distance-K coloring of the graph. With this coloring we can finally simulate Local model algorithms running in a constant number of rounds, using the colors as unique identifiers. Our algorithms work under the Gouda daemon, similar to the probabilistic daemon: if an event should eventually happen, it will occur.
Cite as

Johanne Cohen, Laurence Pilard, Mikaël Rabie, and Jonas Sénizergues. Making Self-Stabilizing Algorithms for Any Locally Greedy Problem. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cohen_et_al:LIPIcs.SAND.2023.11,
  author =	{Cohen, Johanne and Pilard, Laurence and Rabie, Mika\"{e}l and S\'{e}nizergues, Jonas},
  title =	{{Making Self-Stabilizing Algorithms for Any Locally Greedy Problem}},
  booktitle =	{2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-275-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{257},
  editor =	{Doty, David and Spirakis, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2023.11},
  URN =		{urn:nbn:de:0030-drops-179475},
  doi =		{10.4230/LIPIcs.SAND.2023.11},
  annote =	{Keywords: Greedy Problem, Ruling Set, Distance-K Coloring, Self-Stabilizing Algorithm}
}
Document
DOI: 10.4230/LIPIcs.DISC.2022.23
Fault Tolerant Coloring of the Asynchronous Cycle

Authors: Pierre Fraigniaud, Patrick Lambein-Monette, and Mikaël Rabie

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

Abstract
We present a wait-free algorithm for proper coloring the n nodes of the asynchronous cycle C_n, where each crash-prone node starts with its (unique) identifier as input. The algorithm is independent of n ≥ 3, and runs in O(log^*n) rounds in C_n. This round-complexity is optimal thanks to a known matching lower bound, which applies even to synchronous (failure-free) executions. The range of colors used by our algorithm, namely {0,…,4}, is optimal too, thanks to a known lower bound on the minimum number of names for which renaming is solvable wait-free in shared-memory systems, whenever n is a power of a prime. Indeed, our model coincides with the shared-memory model whenever n = 3, and the minimum number of names for which renaming is possible in 3-process shared-memory systems is 5.
Cite as

Pierre Fraigniaud, Patrick Lambein-Monette, and Mikaël Rabie. Fault Tolerant Coloring of the Asynchronous Cycle. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 23:1-23:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fraigniaud_et_al:LIPIcs.DISC.2022.23,
  author =	{Fraigniaud, Pierre and Lambein-Monette, Patrick and Rabie, Mika\"{e}l},
  title =	{{Fault Tolerant Coloring of the Asynchronous Cycle}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{23:1--23:22},
  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.2022.23},
  URN =		{urn:nbn:de:0030-drops-172147},
  doi =		{10.4230/LIPIcs.DISC.2022.23},
  annote =	{Keywords: graph coloring, LOCAL model, shared-memory model, immediate snapshot, renaming, wait-free algorithms}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2021.19
Distributed Recoloring of Interval and Chordal Graphs

Authors: Nicolas Bousquet, Laurent Feuilloley, Marc Heinrich, and Mikaël Rabie

Published in: LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021)

Abstract
One of the fundamental and most-studied algorithmic problems in distributed computing on networks is graph coloring, both in bounded-degree and in general graphs. Recently, the study of this problem has been extended in two directions. First, the problem of recoloring, that is computing an efficient transformation between two given colorings (instead of computing a new coloring), has been considered, both to model radio network updates, and as a useful subroutine for coloring. Second, as it appears that general graphs and bounded-degree graphs do not model real networks very well (with, respectively, pathological worst-case topologies and too strong assumptions), coloring has been studied in more specific graph classes. In this paper, we study the intersection of these two directions: distributed recoloring in two relevant graph classes, interval and chordal graphs. More formally, the question of recoloring a graph is as follows: we are given a network, an input coloring α and a target coloring β, and we want to find a schedule of colorings to reach β starting from α. In a distributed setting, the schedule needs to be found within the LOCAL model, where nodes communicate with their direct neighbors synchronously. The question we want to answer is: how many rounds of communication {are} needed to produce a schedule, and what is the length of this schedule? In the case of interval and chordal graphs, we prove that, if we have less than 2ω colors, ω being the size of the largest clique, extra colors will be needed in the intermediate colorings. For interval graphs, we produce a schedule after O(poly(Δ)log*n) rounds of communication, and for chordal graphs, we need O(ω²Δ²log n) rounds to get one. Our techniques also improve classic coloring algorithms. Namely, we get ω+1-colorings of interval graphs in O(ωlog*n) rounds and of chordal graphs in O(ωlog n) rounds, which improves on previous known algorithms that use ω+2 colors for the same running times.
Cite as

Nicolas Bousquet, Laurent Feuilloley, Marc Heinrich, and Mikaël Rabie. Distributed Recoloring of Interval and Chordal Graphs. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bousquet_et_al:LIPIcs.OPODIS.2021.19,
  author =	{Bousquet, Nicolas and Feuilloley, Laurent and Heinrich, Marc and Rabie, Mika\"{e}l},
  title =	{{Distributed Recoloring of Interval and Chordal Graphs}},
  booktitle =	{25th International Conference on Principles of Distributed Systems (OPODIS 2021)},
  pages =	{19:1--19:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-219-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{217},
  editor =	{Bramas, Quentin and Gramoli, Vincent and Milani, Alessia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.19},
  URN =		{urn:nbn:de:0030-drops-157941},
  doi =		{10.4230/LIPIcs.OPODIS.2021.19},
  annote =	{Keywords: Distributed coloring, distributed recoloring, interval graphs, chordal graphs, intersection graphs}
}
Document
Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management
DOI: 10.4230/LIPIcs.ICALP.2019.135
Distributed Reconfiguration of Maximal Independent Sets

Authors: Keren Censor-Hillel and Mikaël Rabie

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
In this paper, we investigate a distributed maximal independent set (MIS) reconfiguration problem, in which there are two maximal independent sets for which every node is given its membership status, and the nodes need to communicate with their neighbors in order to find a reconfiguration schedule that switches from the first MIS to the second. Such a schedule is a list of independent sets that is restricted by forbidding two neighbors to change their membership status at the same step. In addition, these independent sets should provide some covering guarantee. We show that obtaining an actual MIS (and even a 3-dominating set) in each intermediate step is impossible. However, we provide efficient solutions when the intermediate sets are only required to be independent and 4-dominating, which is almost always possible, as we fully characterize. Consequently, our goal is to pin down the tradeoff between the possible length of the schedule and the number of communication rounds. We prove that a constant length schedule can be found in O(MIS+R32) rounds, where MIS is the complexity of finding an MIS in a worst-case graph and R32 is the complexity of finding a (3,2)-ruling set. For bounded degree graphs, this is O(log^*n) rounds and we show that it is necessary. On the other extreme, we show that with a constant number of rounds we can find a linear length schedule.
Cite as

Keren Censor-Hillel and Mikaël Rabie. Distributed Reconfiguration of Maximal Independent Sets. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 135:1-135:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{censorhillel_et_al:LIPIcs.ICALP.2019.135,
  author =	{Censor-Hillel, Keren and Rabie, Mika\"{e}l},
  title =	{{Distributed Reconfiguration of Maximal Independent Sets}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{135:1--135:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.135},
  URN =		{urn:nbn:de:0030-drops-107111},
  doi =		{10.4230/LIPIcs.ICALP.2019.135},
  annote =	{Keywords: distributed graph algorithms, reconfiguration, maximal independent set}
}
Document
DOI: 10.4230/LIPIcs.DISC.2018.12
Distributed Recoloring

Authors: Marthe Bonamy, Paul Ouvrard, Mikaël Rabie, Jukka Suomela, and Jara Uitto

Published in: LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

Abstract
Given two colorings of a graph, we consider the following problem: can we recolor the graph from one coloring to the other through a series of elementary changes, such that the graph is properly colored after each step? We introduce the notion of distributed recoloring: The input graph represents a network of computers that needs to be recolored. Initially, each node is aware of its own input color and target color. The nodes can exchange messages with each other, and eventually each node has to stop and output its own recoloring schedule, indicating when and how the node changes its color. The recoloring schedules have to be globally consistent so that the graph remains properly colored at each point, and we require that adjacent nodes do not change their colors simultaneously. We are interested in the following questions: How many communication rounds are needed (in the deterministic LOCAL model of distributed computing) to find a recoloring schedule? What is the length of the recoloring schedule? And how does the picture change if we can use extra colors to make recoloring easier? The main contributions of this work are related to distributed recoloring with one extra color in the following graph classes: trees, 3-regular graphs, and toroidal grids.
Cite as

Marthe Bonamy, Paul Ouvrard, Mikaël Rabie, Jukka Suomela, and Jara Uitto. Distributed Recoloring. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bonamy_et_al:LIPIcs.DISC.2018.12,
  author =	{Bonamy, Marthe and Ouvrard, Paul and Rabie, Mika\"{e}l and Suomela, Jukka and Uitto, Jara},
  title =	{{Distributed Recoloring}},
  booktitle =	{32nd International Symposium on Distributed Computing (DISC 2018)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-092-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{121},
  editor =	{Schmid, Ulrich and Widder, Josef},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.12},
  URN =		{urn:nbn:de:0030-drops-98012},
  doi =		{10.4230/LIPIcs.DISC.2018.12},
  annote =	{Keywords: Distributed Systems, Graph Algorithms, Local Computations}
}
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