Exact and FPT algorithms for max-conflict free coloring in hypergraphs

Pradeesha Ashok, Aditi Dudeja, Sudeshna Kolay

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Scopus citations


Conflict-free coloring of hypergraphs is a very well studied question of theoretical and practical interest. For a hypergraph H = (U,F), a conflict-free coloring of H refers to a vertex coloring where every hyperedge has a vertex with a unique color, distinct from all other vertices in the hyperedge. In this paper, we initiate a study of natural maximization version of this problem, namely, Max-CFC: For a given hypergraph H and a fixed r ≥ 2, color the vertices of U using r colors so that the number of hyperedges that are conflict-free colored is maximized. By previously known hardness results for conflict-free coloring, this maximization version is NP-hard. We study this problem in the context of both exact and parameterized algorithms. In the parameterized setting, we study this problem with respect to the natural parameter, the solution size. In particular, we study the following question: p-CFC: For a given hypergraph, can we conflict-free color at least k hyperedges with at most r colors, the parameter being k. We show that this problem is FPT by designing an algorithm with running time 2O(k log log k+k log r)(n+m)O(1) using a novel connection to the Unique Coverage problem and applying the method of color coding in a non-trivial manner. For the special case for hypergraphs induced by graph neighbourhoods we give a polynomial kernel. Finally, we give an exact algorithm for Max-CFC running in O(2n+m) time. All our algorithms, with minor modifications, work for a stronger version of conflict-free coloring, Unique Maximum Coloring.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 26th International Symposium, ISAAC 2015, Proceedings
EditorsKhaled Elbassioni, Kazuhisa Makino
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783662489703
StatePublished - 1 Jan 2015
Externally publishedYes
Event26th International Symposium on Algorithms and Computation, ISAAC 2015 - Nagoya, Japan
Duration: 9 Dec 201511 Dec 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference26th International Symposium on Algorithms and Computation, ISAAC 2015

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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