Isomorphism for Graphs of Bounded Distance Width

In this paper, we study the Graph Isomorphism problem on graphs of bounded treewidth, bounded degree or bounded bandwidth. Graph Isomorphism can be solved in polynomial time for graphs of bounded treewidth, pathwidth, or bandwidth, but the exponent depends on the treewidth, pathwidth, or bandwidth. Thus, we look for special cases where ` xed parameter tractable' polynomial time algorithms can be established. We introduce some new and natural graph parameters: the rooted path distance width, which is a restriction of bandwidth, and the rooted tree distance width, which is a restriction of treewidth. We give algorithms that solve Graph Isomorphism in On2 time for graphs with bounded rooted path distance width, and in On3 time for graphs with bounded rooted tree distance width. Additionally, we show that computing the path distance width of a graph is NP-hard, but both path and tree distance width can be computed in Onk+1 time, when they are bounded by a constant k; the ro...

• Type: Conference
• Year: 1997
• Where: CIAC
• Authors: Koichi Yamazaki, Hans L. Bodlaender, Babette de Fluiter, Dimitrios M. Thilikos
• Keywords: Algorithms, CIAC 1997, Distance Width, Path Distance Width, Tree Distance Width