Representative families: A unified tradeoff-based approach

Given a matroid M=(E,I), and a family S of p-subsets of E, a subfamily Sˆ⊆S represents S if for any X∈S and Y⊆E∖X satisfying X∪Y∈I, there is a set Xˆ∈Sˆ disjoint from Y, where Xˆ∪Y∈I. We show that a powerful technique for computing representative families, introduced by Fomin et al. (2014) [5], lead...

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Vydáno v:Journal of computer and system sciences Ročník 82; číslo 3; s. 488 - 502
Hlavní autoři: Shachnai, Hadas, Zehavi, Meirav
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.05.2016
Témata:
k-Internal out-branching
k-Partial cover
Parameterized algorithm
Representative family
Uniform matroid
k-IOB
k-Internal out-branching
k-PC
Representative family
Uniform matroid
Parameterized algorithm
k-Partial cover
ISSN:0022-0000, 1090-2724
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Popis
Shrnutí:Given a matroid M=(E,I), and a family S of p-subsets of E, a subfamily Sˆ⊆S represents S if for any X∈S and Y⊆E∖X satisfying X∪Y∈I, there is a set Xˆ∈Sˆ disjoint from Y, where Xˆ∪Y∈I. We show that a powerful technique for computing representative families, introduced by Fomin et al. (2014) [5], leads to a unified approach for substantially improving the running times of parameterized algorithms for some classic problems. This includes k-Partial Cover, k-Internal Out-Branching, and Long Directed Cycle, among others. Our approach exploits an interesting tradeoff between running time and the representative family size. •A unified tradeoff-based approach for computing representative families.•Faster FPT algorithms for problems previously solved by using representative families.•Fastest FPT algorithm for the k-Partial Cover problem.•Faster deterministic FPT algorithm for the k-Internal Out-Branching problem.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2015.11.008