We give an fpt approximation algorithm for the directed vertex disjoint cycle problem. Given a directed graph G with n vertices and a positive integer k, the algorithm constructs a family of at least k/ρ(k) disjoint cycles of G if the graph G has a family of at least k disjoint cycles (and otherwise may still produce a solution, or just report failure). Here ρ is a computable function such that k/ρ(k) is nondecreasing and unbounded. The running time of our algorithm is polynomial. The directed vertex disjoint cycle problem is hard for the parameterized complexity class W[1], and to the best of our knowledge our algorithm is the first fpt approximation algorithm for a natural W[1]-hard problem. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Grohe, M., & Grüber, M. (2007). Parameterized approximability of the disjoint cycle problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4596 LNCS, pp. 363–374). Springer Verlag. https://doi.org/10.1007/978-3-540-73420-8_33
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