Measuring indifference: unit interval vertex deletion

  • Authors:

  • René Van Bevern;Christian Komusiewicz;Hannes Moser;Rolf Niedermeier

  • Affiliations:

  • Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany

  • Venue:
  • WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
  • Year:
  • 2010

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Abstract

Making a graph unit interval by a minimum number of vertex deletions is NP-hard. The problem is motivated by applications in seriation and measuring in difference between data items. We present a fixed-parameter algorithm based on the iterative compression technique that finds in O((14k+14)k+1kn6) time a set of k vertices whose deletion from an n-vertex graph makes it unit interval. Additionally, we show that making a graph chordal by at most k vertex deletions is NP-complete even on {claw, net, tent}-free graphs.