2 Search Results for "Villani, Neven"

Document

DOI: 10.4230/LIPIcs.OPODIS.2024.33

Self-Stabilizing Fully Adaptive Maximal Matching

Authors: Shimon Bitton, Yuval Emek, Taisuke Izumi, and Shay Kutten

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

Abstract

A self-stabilizing randomized algorithm for mending maximal matching (MM) in synchronous networks is presented. Starting from a legal MM configuration and assuming that the network undergoes k faults or topology changes (that may occur in multiple batches), the algorithm is guaranteed to stabilize back to a legal MM configuration in time O(log k) in expectation and with high probability (in k), using constant size messages. The algorithm is simple to implement and is uniform in the sense that it does not assume unique identifiers, nor does it assume any global knowledge of the communication graph including its size. It relies on a generic probabilistic phase synchronization technique that may be useful for other self-stabilizing problems. The algorithm compares favorably with the existing self-stabilizing MM algorithms in terms of the dependence of its run-time on k, a.k.a. fully adaptive run-time. In fact, this dependence is asymptotically optimal for uniform algorithms that use constant size messages.

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Shimon Bitton, Yuval Emek, Taisuke Izumi, and Shay Kutten. Self-Stabilizing Fully Adaptive Maximal Matching. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bitton_et_al:LIPIcs.OPODIS.2024.33,
  author =	{Bitton, Shimon and Emek, Yuval and Izumi, Taisuke and Kutten, Shay},
  title =	{{Self-Stabilizing Fully Adaptive Maximal Matching}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{33:1--33:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.33},
  URN =		{urn:nbn:de:0030-drops-225698},
  doi =		{10.4230/LIPIcs.OPODIS.2024.33},
  annote =	{Keywords: self-stabilization, maximal matching, fully adaptive run-time, dynamic graphs}
}

Document

DOI: 10.4230/LIPIcs.OPODIS.2022.21

Mending Partial Solutions with Few Changes

Authors: Darya Melnyk, Jukka Suomela, and Neven Villani

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

Abstract

In this paper, we study the notion of mending: given a partial solution to a graph problem, how much effort is needed to take one step towards a proper solution? For example, if we have a partial coloring of a graph, how hard is it to properly color one more node? In prior work (SIROCCO 2022), this question was formalized and studied from the perspective of mending radius: if there is a hole that we need to patch, how far do we need to modify the solution? In this work, we investigate a complementary notion of mending volume: how many nodes need to be modified to patch a hole? We focus on the case of locally checkable labeling problems (LCLs) in trees, and show that already in this setting there are two infinite hierarchies of problems: for infinitely many values 0 < α ≤ 1, there is an LCL problem with mending volume Θ(n^α), and for infinitely many values k ≥ 1, there is an LCL problem with mending volume Θ(log^k n). Hence the mendability of LCL problems on trees is a much more fine-grained question than what one would expect based on the mending radius alone.

Cite as

Darya Melnyk, Jukka Suomela, and Neven Villani. Mending Partial Solutions with Few Changes. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 253, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{melnyk_et_al:LIPIcs.OPODIS.2022.21,
  author =	{Melnyk, Darya and Suomela, Jukka and Villani, Neven},
  title =	{{Mending Partial Solutions with Few Changes}},
  booktitle =	{26th International Conference on Principles of Distributed Systems (OPODIS 2022)},
  pages =	{21:1--21:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-265-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{253},
  editor =	{Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2022.21},
  URN =		{urn:nbn:de:0030-drops-176413},
  doi =		{10.4230/LIPIcs.OPODIS.2022.21},
  annote =	{Keywords: mending, LCL problems, volume model}
}

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2 Search Results for "Villani, Neven"

Self-Stabilizing Fully Adaptive Maximal Matching

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Mending Partial Solutions with Few Changes

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