A 2-Approximation algorithm for the undirected feedback vertex set problem

Vineet Bafna, Piotr Berman, Toshihiro Fujito

    Research output: Contribution to journalArticlepeer-review

    267 Scopus citations


    A feedback vertex set of a graph is a subset of vertices that contains at least one vertex from every cycle in the graph. The problem considered is that of finding a minimum feedback vertex set given a weighted and undirected graph. We present a simple and efficient approximation algorithm with performance ratio of at most 2, improving previous best bounds for either weighted or unweighted cases of the problem. Any further improvement on this bound, matching the best constant factor known for the vertex cover problem, is deemed challenging. The approximation principle, underlying the algorithm, is based on a generalized form of the classical local ratio theorem, originally developed for approximation of the vertex cover problem, and a more flexible style of its application.

    Original languageEnglish (US)
    Pages (from-to)289-297
    Number of pages9
    JournalSIAM Journal on Discrete Mathematics
    Issue number3
    StatePublished - Sep 1999

    All Science Journal Classification (ASJC) codes

    • Mathematics(all)


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