Faster FPT Algorithm for 5-Path Vertex Cover

06/21/2019

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by   Radovan Červený, et al.

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The problem of d-Path Vertex Cover, d-PVC lies in determining a subset F of vertices of a given graph G=(V,E) such that G ∖ F does not contain a path on d vertices. The paths we aim to cover need not to be induced. It is known that the d-PVC problem is NP-complete for any d > 2. When parameterized by the size of the solution k, 5-PVC has direct trivial algorithm with O(5^kn^O(1)) running time and, since d-PVC is a special case of d-Hitting Set, an algorithm running in O(4.0755^kn^O(1)) time is known. In this paper we present an iterative compression algorithm that solves the 5-PVC problem in O(4^kn^O(1)) time.