Cutwidth I: a linear time fixed parameter algorithm

  • Authors:

  • Dimitrios M. Thilikos;Maria Serna;Hans L. Bodlaender

  • Affiliations:

  • Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Barcelona, Spain;Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Barcelona, Spain;Department of Computer Science, Utrecht University, TB Utrecht, The Netherlands

  • Venue:
  • Journal of Algorithms
  • Year:
  • 2005

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Abstract

The cutwidth of a graph G is the smallest integer k such that the vertices of G can be arranged in a linear layout [v1,...,vn] in such a way that, for every i = 1,...,n - 1, there are at most k edges with one endpoint in {v1.....vi}. and the other in {vi+1,...,vn}. In this paper we provide, for any constant k, a linear time algorithm that for any input graph G, answers whether G has cutwidth at most k and, in the case of a positive answer, outputs the corresponding linear layout.