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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Bibliographic Details
Published in:	Journal of computer and system sciences Vol. 82; no. 3; pp. 488 - 502
Main Authors:	Shachnai, Hadas, Zehavi, Meirav
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.05.2016
Subjects:	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
Online Access:	Get full text
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Summary:	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