Feedback Vertex Set on Graphs of Low Cliquewidth

The Feedback Vertex Set problem asks whether a graph contains q vertices meeting all its cycles. This is not a local property, in the sense that we cannot check if q vertices meet all cycles by looking only at their neighbors. Dynamic programming algorithms for problems based on non-local properties are usually more complicated. In this paper, given a graph G of cliquewidth cw and a cw-expression of G, we solve the Minimum Feedback Vertex Set problem in time O(n2 22cw2 log cw ). Our algorithm applies a non-standard dynamic programming on a so-called k-module decomposition of a graph, as defined by Rao [28], which is easily derivable from a k-expression of the graph. The related notion of module-width of a graph is tightly linked to both cliquewidth and nlc-width, and in this paper we give an alternative equivalent characterization of module-width.

• Type: Conference
• Year: 2009
• Where: IWOCA
• Authors: Binh-Minh Bui-Xuan, Jan Arne Telle, Martin Vatshelle
• Keywords: Algorithms, Dynamic Programming, Feedback Vertex Set, IWOCA 2009, Vertex Set Problem