Cutwidth II: algorithms for partial w-trees of bounded degree

  • 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 defined to be the smallest integer k such that the vertices of G can be arranged in a vertex ordering [v1,...,vn] in 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}. We examine the problem of computing in polynomial time the cutwidth of a partial w-tree with bounded degree. In particular, we show how to construct an algorithm that, in nO(w2d) steps, computes the cutwidth of any partial w-tree with vertices of degree bounded by a fixed constant d. Our algorithm is constructive in the sense that it can be adapted to output a corresponding optimal vertex ordering. Also, it is the main subroutine of an algorithm computing the pathwidth of a bounded degree partial w-tree with the same time complexity.