Improved algorithms for feedback vertex set problems

Authors:
Jianer Chen;Fedor V. Fomin;Yang Liu;Songjian Lu;Yngve Villanger
Affiliations:
Department of Computer Science, Texas A&M University, College Station, TX 77843-3112, USA;Department of Informatics, University of Bergen, N-5020 Bergen, Norway;Department of Computer Science, Texas A&M University, College Station, TX 77843-3112, USA;Department of Computer Science, Texas A&M University, College Station, TX 77843-3112, USA;Department of Informatics, University of Bergen, N-5020 Bergen, Norway
Venue:
Journal of Computer and System Sciences
Year:
2008

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Abstract

We present improved parameterized algorithms for the feedback vertex set problem on both unweighted and weighted graphs. Both algorithms run in time O(5^kkn^2). The algorithms construct a feedback vertex set of size at most k (in the weighted case this set is of minimum weight among the feedback vertex sets of size at most k) in a given graph G of n vertices, or report that no such feedback vertex set exists in G.