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Documents authored by Lambein-Monette, Patrick

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.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.SAND.2022.10
Computing Outside the Box: Average Consensus over Dynamic Networks

Authors: Bernadette Charron-Bost and Patrick Lambein-Monette

Published in: LIPIcs, Volume 221, 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)

Abstract
Networked systems of autonomous agents, and applications thereof, often rely on the control primitive of average consensus, where the agents are to compute the average of private initial values. To provide reliable services that are easy to deploy, average consensus should continue to operate when the network is subject to frequent and unpredictable change, and should mobilize few computational resources, so that deterministic, low powered, and anonymous agents can partake in the network. In this stringent adversarial context, we investigate the implementation of average consensus by distributed algorithms over networks with bidirectional, but potentially short-lived, communication links. Inspired by convex recurrence rules for multi-agent systems, and the Metropolis average consensus rule in particular, we design a deterministic distributed algorithm that achieves asymptotic average consensus, which we show to operate in polynomial time in a synchronous temporal model. The algorithm is easy to implement, has low space and computational complexity, and is fully distributed, requiring neither symmetry-breaking devices like unique identifiers, nor global control or knowledge of the network. In the fully decentralized model that we adopt, to our knowledge, no other distributed average consensus algorithm has a better temporal complexity. Our approach distinguishes itself from classical convex recurrence rules in that the agent’s values may sometimes leave their previous convex hull. As a consequence, our convergence bound requires a subtle analysis, despite the syntactic simplicity of our algorithm.
Cite as

Bernadette Charron-Bost and Patrick Lambein-Monette. Computing Outside the Box: Average Consensus over Dynamic Networks. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{charronbost_et_al:LIPIcs.SAND.2022.10,
  author =	{Charron-Bost, Bernadette and Lambein-Monette, Patrick},
  title =	{{Computing Outside the Box: Average Consensus over Dynamic Networks}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{10:1--10:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.10},
  URN =		{urn:nbn:de:0030-drops-159521},
  doi =		{10.4230/LIPIcs.SAND.2022.10},
  annote =	{Keywords: average consensus, dynamic networks, distributed algorithms, iterated averaging, Metropolis}
}
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