Better Polynomial Algorithms on Graphs of Bounded Rank-Width

Abstract. Although there exist many polynomial algorithms for NPhard problems running on a bounded clique-width expression of the input graph, there exists only little comparable work on such algorithms for rank-width. We believe that one reason for this is the somewhat obscure and hard-to-grasp nature of rank-decompositions. Nevertheless, strong arguments for using the rank-width parameter have been given by recent formalisms independently developed by Courcelle and Kant´e, by the authors, and by Bui-Xuan et al. This article focuses on designing formally clean and understandable “pseudopolynomial” (XP) algorithms solving “hard” problems (non-FPT) on graphs of bounded rank-width. Those include computing the chromatic number and polynomial or testing the Hamiltonicity of a graph and are extendable to many other problems.

• Type: Conference
• Year: 2009
• Where: IWOCA
• Authors: Robert Ganian, Petr Hlinený
• Keywords: Algorithms, Input Graph, IWOCA 2009, Little Comparable Work, Polynomial Algorithms