Bandwidth of bipartite permutation graphs in polynomial time

Authors:
Pinar Heggernes;Dieter Kratsch;Daniel Meister
Affiliations:
Department of Informatics, University of Bergen, PO Box 7803, N-5020 Bergen, Norway;Laboratoire d'Informatique Théorique et Appliquée, Université Paul Verlaine, Metz, 57045 Metz Cedex 01, France;Department of Informatics, University of Bergen, PO Box 7803, N-5020 Bergen, Norway
Venue:
Journal of Discrete Algorithms
Year:
2009

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Abstract

We give the first polynomial-time algorithm that computes the bandwidth of bipartite permutation graphs. Bandwidth is an NP-complete graph layout problem that is notorious for its difficulty even on small graph classes. For example, it remains NP-complete on caterpillars of hair length at most 3, a very restricted subclass of trees. Much attention has been given to designing approximation algorithms for computing the bandwidth, as it is NP-hard to approximate the bandwidth of general graphs with a constant factor guarantee. The problem is considered important even for approximation on restricted classes, with several distinguished results in this direction. Prior to our work, polynomial-time algorithms for exact computation of bandwidth were known only for caterpillars of hair length at most 2, chain graphs, cographs, and most interestingly, interval graphs.