Parameterized Approximability of the Disjoint Cycle Problem
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 W1, and to the best of our knowledge our algorithm is the first fpt approximation algorithm for a natural W1-hard problem.
Keywordsapproximation algorithms fixed-parameter tractability parameterized complexity theory
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