Online conflict-free colouring for hypergraphs

A. Bar-Noy, P. Cheilaris, S. Olonetsky, S. Smorodinsky

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

We provide a framework for online conflict-free colouring of any hypergraph. We introduce the notion of a degenerate hypergraph, which characterizes hypergraphs that arise in geometry. We use our framework to obtain an efficient randomized online algorithm for conflict-free colouring of any k-degenerate hypergraph with n vertices. Our algorithm uses O(k log n) colours with high probability and this bound is asymptotically optimal. Moreover, our algorithm uses O(k log k log n) random bits with high probability. We introduce algorithms that are allowed to perform a few recolourings of already coloured points. We provide deterministic online conflict-free colouring algorithms for points on the line with respect to intervals and for points on the plane with respect to half-planes (or unit disks) that use O(log n) colours and perform a total of at most O(n) recolourings.

Original languageEnglish
Pages (from-to)493-516
Number of pages24
JournalCombinatorics Probability and Computing
Volume19
Issue number4
DOIs
StatePublished - 1 Jul 2010

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics

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