eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-08-20
32:1
32:13
10.4230/LIPIcs.MFCS.2019.32
article
Faster FPT Algorithm for 5-Path Vertex Cover
Červený, Radovan
1
https://orcid.org/0000-0003-4528-9525
Suchý, Ondřej
1
https://orcid.org/0000-0002-7236-8336
Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Prague, Czech Republic
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol138-mfcs2019/LIPIcs.MFCS.2019.32/LIPIcs.MFCS.2019.32.pdf
graph algorithms
Hitting Set
iterative compression
parameterized complexity
d-Path Vertex Cover