Conflict-free coloring with respect to a subset of intervals

Panagiotis Cheilaris, Shakhar Smorodinsky

Research output: Working paper/PreprintPreprint

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Abstract

Given a hypergraph H = (V, E), a coloring of its vertices is said to be conflict-free if for every hyperedge S \in E there is at least one vertex in S whose color is distinct from the colors of all other vertices in S. The discrete interval hypergraph Hn is the hypergraph with vertex set {1,...,n} and hyperedge set the family of all subsets of consecutive integers in {1,...,n}. We provide a polynomial time algorithm for conflict-free coloring any subhypergraph of Hn, we show that the algorithm has approximation ratio 2, and we prove that our analysis is tight, i.e., there is a subhypergraph for which the algorithm computes a solution which uses twice the number of colors of the optimal solution. We also show that the problem of deciding whether a given subhypergraph of Hn can be colored with at most k colors has a quasipolynomial time algorithm.
Original languageEnglish GB
PublisherarXiv:1204.6422 [math.CO]
Number of pages11
StatePublished - 2012

Keywords

  • math.CO
  • cs.DM
  • cs.DS

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