DROPS

Document

DOI: 10.4230/LIPIcs.STACS.2020.52

Perfect Resolution of Conflict-Free Colouring of Interval Hypergraphs

Authors: S. M. Dhannya and N. S. Narayanaswamy

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)

Abstract

Given a hypergraph H, the conflict-free colouring problem is to colour vertices of H using minimum colours so that in every hyperedge e of H, there is a vertex whose colour is different from that of all other vertices in e. Our results are on a variant of the conflict-free colouring problem considered by Cheilaris et al.[Cheilaris et al., 2014], known as the 1-Strong Conflict-Free (1-SCF) colouring problem, for which they presented a polynomial time 2-approximation algorithm for interval hypergraphs. We show that an optimum 1-SCF colouring for interval hypergraphs can be computed in polynomial time. Our results are obtained by considering a different view of conflict-free colouring which we believe could be useful in general. For interval hypergraphs, this different view brings a connection to the theory of perfect graphs which is useful in coming up with an LP formulation to select the vertices that could be coloured to obtain an optimum conflict-free colouring. The perfect graph connection again plays a crucial role in finding a minimum colouring for the vertices selected by the LP formulation.

Cite as

S. M. Dhannya and N. S. Narayanaswamy. Perfect Resolution of Conflict-Free Colouring of Interval Hypergraphs. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 52:1-52:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{dhannya_et_al:LIPIcs.STACS.2020.52,
  author =	{Dhannya, S. M. and Narayanaswamy, N. S.},
  title =	{{Perfect Resolution of Conflict-Free Colouring of Interval Hypergraphs}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{52:1--52:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.52},
  URN =		{urn:nbn:de:0030-drops-119138},
  doi =		{10.4230/LIPIcs.STACS.2020.52},
  annote =	{Keywords: Conflict-free Colouring, Interval Hypergraphs}
}

Search Results

Documents authored by Dhannya, S. M.

Perfect Resolution of Conflict-Free Colouring of Interval Hypergraphs

Abstract

Cite as

Thanks for your feedback!

Could not send message