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

Given a graph G and a parameter k∈N, 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, V...

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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 81; no. 1; pp. 186 - 207
Main Authors: Kim, Eun Jung, Paul, Christophe, Philip, Geevarghese
Format: Journal Article
Language:English
Published: Elsevier Inc 01.02.2015
Elsevier
Subjects:
[formula omitted]-minor cover
Computer Science
Discrete Mathematics
Fixed-parameter tractable algorithms
Treewidth-2 Deletion
Treewidth-2 Deletion
Fixed-parameter tractable algorithms
K4-minor cover
FPT time
Vertex Cover
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary:Given a graph G and a parameter k∈N, 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-tVertex 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-tVertex Deletion can be solved in time 2o(k)⋅nO(1). •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.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2014.05.001