Abstract
Given a matroid M=(E,I), and a family S of p-subsets of E, a subfamily ͈⊆S represents S if for any X∈S and Y⊆E\X satisfying X∪Y∈I, there is a set X∈͈ disjoint from Y, where X∪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.
Original language | English |
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Pages (from-to) | 488-502 |
Number of pages | 15 |
Journal | Journal of Computer and System Sciences |
Volume | 82 |
Issue number | 3 |
DOIs | |
State | Published - 1 Jan 2016 |
Externally published | Yes |
Keywords
- Parameterized algorithm
- Representative family
- Uniform matroid
- k-Internal out-branching
- k-Partial cover
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics