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Faster FPT Algorithm for 5-Path Vertex Cover

Authors Radovan Červený , Ondřej Suchý



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Author Details

Radovan Červený
  • Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Prague, Czech Republic
Ondřej Suchý
  • Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Prague, Czech Republic

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Radovan Červený and Ondřej Suchý. Faster FPT Algorithm for 5-Path Vertex Cover. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 32:1-32:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.MFCS.2019.32

Abstract

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Fixed parameter tractability
Keywords
  • graph algorithms
  • Hitting Set
  • iterative compression
  • parameterized complexity
  • d-Path Vertex Cover

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