Parameterized Approximability of the Disjoint Cycle Problem

Abstract. 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. Key words: approximation algorithms, fixed-parameter tractability, parameterized complexity theory.

• Type: Conference
• Year: 2007
• Where: ICALP
• Authors: Martin Grohe, Magdalena Grüber
• Keywords: Directed Vertex Disjoint, Disjoint Cycle, ICALP 2007, Theoretical Computer Science, Vertex Disjoint Cycle