On the OBDD size for graphs of bounded tree- and clique-width

  • Authors:

  • Klaus Meer;Dieter Rautenbach

  • Affiliations:

  • Department of Mathematics and Computer Science, Syddansk Universitet, Odense M, Denmark;Forschungsinstitut für Diskrete Mathematik, Universität Bonn, Bonn, Germany

  • Venue:
  • IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
  • Year:
  • 2006

Quantified Score

Hi-index 0.00

Visualization

Abstract

We study the size of OBDDs (ordered binary decision diagrams) for representing the adjacency function fG of a graph G on n vertices. Our results are as follows: -) For graphs of bounded tree-width there is an OBDD of size O(logn) for fG that uses encodings of size O(logn) for the vertices; -) For graphs of bounded clique-width there is an OBDD of size O(n) for fG that uses encodings of size O(n) for the vertices; -) For graphs of bounded clique-width such that there is a reduced term for G (to be defined below) that is balanced with depth O(logn) there is an OBDD of size O(n) for fG that uses encodings of size O(logn) for the vertices; -) For cographs, i.e. graphs of clique-width at most 2, there is an OBDD of size O(n) for fG that uses encodings of size O(logn) for the vertices. This last result improves a recent result by Nunkesser and Woelfel [14].