Better Polynomial Algorithms on Graphs of Bounded Rank-width.
|Year of publication||2009|
|Type||Article in Proceedings|
|Conference||IWOCA 2009: International Workshop On Combinatorial Algorithms, Lecture Notes in Computer Science 5874|
|MU Faculty or unit|
|Keywords||rank-width; parameterized algorithms; graphs|
|Description||Although there exist many polynomial algorithms for NP-hard 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 Kante, 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.|