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, Campus Nord -- Edifici Ω, c/Jordi Girona Salgado 1-3, 08034 Barcelona, Spain;Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Campus Nord -- Edifici Ω, c/Jordi Girona Salgado 1-3, 08034 Barcelona, Spain;Department of Computer Science, Utrecht University, P.O. Box 80.089, 3508 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 [v"1,...,v"n] in a way that, for every i=1,...,n-1, there are at most k edges with one endpoint in {v"1,...,v"i} and the other in {v"i"+"1,...,v"n}. 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 n^O^(^w^^^2^d^) 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.