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

Authors Andrzej Dorobisz , Jakub Kozik



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Author Details

Andrzej Dorobisz
  • Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Jakub Kozik
  • Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland

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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)
https://doi.org/10.4230/LIPIcs.ICALP.2023.48

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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Hypergraphs
  • Mathematics of computing → Probabilistic algorithms
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Local Computation Algorithms
  • Hypergraph Coloring
  • Property B

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References

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