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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2023.48

Local Computation Algorithms for Hypergraph Coloring - Following Beck’s Approach

Authors: Andrzej Dorobisz and Jakub Kozik

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract

We investigate local computation algorithms (LCA) for two-coloring of k-uniform hypergraphs. We focus on hypergraph instances that satisfy strengthened assumption of the Lovász Local Lemma of the form 2^(1-αk) (Δ+1) e < 1, where Δ is the bound on the maximum edge degree. The main question which arises here is for how large α there exists an LCA that is able to properly color such hypergraphs in polylogarithmic time per query. We describe briefly how upgrading the classical sequential procedure of Beck from 1991 with Moser and Tardos' Resample yields polylogarithmic LCA that works for α up to 1/4. Then, we present an improved procedure that solves wider range of instances by allowing α up to 1/3.

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Andrzej Dorobisz and Jakub Kozik. Local Computation Algorithms for Hypergraph Coloring - Following Beck’s Approach. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 48:1-48:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dorobisz_et_al:LIPIcs.ICALP.2023.48,
  author =	{Dorobisz, Andrzej and Kozik, Jakub},
  title =	{{Local Computation Algorithms for Hypergraph Coloring - Following Beck’s Approach}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{48:1--48:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.48},
  URN =		{urn:nbn:de:0030-drops-181002},
  doi =		{10.4230/LIPIcs.ICALP.2023.48},
  annote =	{Keywords: Local Computation Algorithms, Hypergraph Coloring, Property B}
}

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Local Computation Algorithms for Hypergraph Coloring - Following Beck’s Approach

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