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IWOCA
2009
Springer

Feedback Vertex Set on Graphs of Low Cliquewidth

9 years 8 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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