A single-exponential FPT algorithm for the K4-minor cover problem

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Highlights

  • We provide an efficient FPT algorithm for the K4-minor cover problem.

  • It combines iterative compression with protrusion reduction and branching.

  • It extends previous algorithms for Vertex Cover and Feedback Vertex Set.

Abstract

Given a graph G and a parameter kN, the parameterized K4-minor cover problem asks whether at most k vertices can be deleted to turn G into a K4-minor-free graph, or equivalently in a graph of treewidth at most 2. This problem is inspired by two well-studied parameterized vertex deletion problems, Vertex Cover and Feedback Vertex Set, which can also be expressed as Treewidth-t Vertex Deletion problems: t=0 for Vertex Cover and t=1 for Feedback Vertex Set. While single-exponential FPT algorithms, i.e. running in 2O(k)nO(1) time, are known for these two latter problems, it was open whether the K4-minor cover problem could be solved in single-exponential FPT time. This paper answers this question in the affirmative. Observe that it is known to be unlikely that Treewidth-t Vertex Deletion can be solved in time 2o(k)nO(1).

Keywords

Treewidth-2 Deletion
Fixed-parameter tractable algorithms
K4-minor cover

Cited by (0)

Eun Jung Kim and Christophe Paul were supported by the ANR project AGAPE (ANR-09-BLAN-0159). Christophe Paul is granted by the Languedoc-Roussillon programme “Chercheur d'Avenir” KERNEL. The research of Geevarghese Philip was supported by the Indo-German Max Planck Center for Computer Science (IMPECS). Bundesministerium für Bildung und Forschung (BMBF) grant number 01OA1001.