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...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Journal of computer and system sciences Ročník 81; číslo 1; s. 186 - 207
Hlavní autoři: Kim, Eun Jung, Paul, Christophe, Philip, Geevarghese
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.02.2015
Elsevier
Témata:
[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
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí: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