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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| Vydané v: | Journal of computer and system sciences Ročník 82; číslo 3; s. 488 - 502 |
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| Jazyk: | English |
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Elsevier Inc
01.05.2016
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| ISSN: | 0022-0000, 1090-2724 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Shachnai, Hadas Zehavi, Meirav |
| Author_xml | – sequence: 1 givenname: Hadas surname: Shachnai fullname: Shachnai, Hadas email: hadas@cs.technion.ac.il – sequence: 2 givenname: Meirav surname: Zehavi fullname: Zehavi, Meirav email: meizeh@cs.technion.ac.il |
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| Cites_doi | 10.1007/s00373-010-0973-2 10.1137/140981290 10.1007/BF01904851 10.1016/S0020-0190(02)00434-9 10.1016/j.tcs.2005.10.008 10.1007/s00453-011-9555-9 10.1016/j.jcss.2010.01.001 10.1016/j.tcs.2009.07.027 10.1007/s00453-011-9575-5 10.1016/j.endm.2010.05.153 10.1016/j.ipl.2011.05.016 10.1016/j.jcss.2012.03.004 10.1016/j.tcs.2009.03.036 |
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