Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization


We show that the NP-complete Feedback Vertex Set problem, which asks for the smallest set of vertices to remove from a graph to destroy all cycles, is deterministically solvable in O(c ·m) time. Here, m denotes the number of graph edges, k denotes the size of the feedback vertex set searched for, and c is a constant. We extend this to an algorithm enumerating all solutions in O(d ·m) time for a (larger) constant d. As a further result, we present a fixed-parameter algorithm with runtime O(2 ·m2) for the NP-complete Edge Bipartization problem, which asks for at most k edges to remove from a graph to make it bipartite.

DOI: 10.1016/j.jcss.2006.02.001

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@article{Guo2006CompressionbasedFA, title={Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization}, author={Jiong Guo and Jens Gramm and Falk H{\"{u}ffner and Rolf Niedermeier and Sebastian Wernicke}, journal={J. Comput. Syst. Sci.}, year={2006}, volume={72}, pages={1386-1396} }