A fixed-parameter algorithm for the directed feedback vertex set problem

Authors:
Jianer Chen;Yang Liu;Songjian Lu;Barry O'sullivan;Igor Razgon
Affiliations:
Texas A&M University, College Station, Texas;Texas A&M University, College Station, Texas;Texas A&M University, College Station, Texas;University College Cork, Cork, Ireland;University College Cork, Cork, Ireland
Venue:
Journal of the ACM (JACM)
Year:
2008

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Abstract

The (parameterized) FEEDBACK VERTEX SET problem on directed graphs (i.e., the DFVS problem) is defined as follows: given a directed graph G and a parameter k, either construct a feedback vertex set of at most k vertices in G or report that no such a set exists. It has been a well-known open problem in parameterized computation and complexity whether the DFVS problem is fixed-parameter tractable, that is, whether the problem can be solved in time f(k)nO(1) for some function f. In this article, we develop new algorithmic techniques that result in an algorithm with running time 4k k! nO(1) for the DFVS problem. Therefore, we resolve this open problem.