Computing the Cutwidth of Bipartite Permutation Graphs in Linear Time

  • Pinar Heggernes
  • Pim van ’t Hof
  • Daniel Lokshtanov
  • Jesper Nederlof
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6410)

Abstract

The problem of determining the cutwidth of a graph is a notoriously hard problem which remains NP-complete under severe restrictions on input graphs. Until recently, non-trivial polynomial-time cutwidth algorithms were known only for subclasses of graphs of bounded treewidth. In WG 2008, Heggernes et al. initiated the study of cutwidth on graph classes containing graphs of unbounded treewidth, and showed that a greedy algorithm computes the cutwidth of threshold graphs. We continue this line of research and present the first polynomial-time algorithm for computing the cutwidth of bipartite permutation graphs. Our algorithm runs in linear time. We stress that the cutwidth problem is NP-complete on bipartite graphs and its computational complexity is open even on small subclasses of permutation graphs, such as trivially perfect graphs.

Keywords

Bipartite Graph Linear Time Input Graph Complete Bipartite Graph Color Classis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Pinar Heggernes
    • 1
  • Pim van ’t Hof
    • 2
  • Daniel Lokshtanov
    • 1
  • Jesper Nederlof
    • 1
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.School of Engineering and Computing Sciences, Science LaboratoriesDurham UniversityDurhamUnited Kingdom

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