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IWOCA
2009
Springer

Feedback Vertex Set on Graphs of Low Cliquewidth

13 years 10 months ago
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.
Binh-Minh Bui-Xuan, Jan Arne Telle, Martin Vatshel
Added 27 May 2010
Updated 27 May 2010
Type Conference
Year 2009
Where IWOCA
Authors Binh-Minh Bui-Xuan, Jan Arne Telle, Martin Vatshelle
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