TY - JOUR
T1 - Representative families
T2 - A unified tradeoff-based approach
AU - Shachnai, Hadas
AU - Zehavi, Meirav
N1 - Funding Information:
We thank the anonymous referees for valuable comments on the paper.
Publisher Copyright:
© 2015 Elsevier Inc. All rights reserved.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - 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.
AB - 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.
KW - Parameterized algorithm
KW - Representative family
KW - Uniform matroid
KW - k-Internal out-branching
KW - k-Partial cover
UR - http://www.scopus.com/inward/record.url?scp=84949256446&partnerID=8YFLogxK
U2 - 10.1016/j.jcss.2015.11.008
DO - 10.1016/j.jcss.2015.11.008
M3 - Article
AN - SCOPUS:84949256446
VL - 82
SP - 488
EP - 502
JO - Journal of Computer and System Sciences
JF - Journal of Computer and System Sciences
SN - 0022-0000
IS - 3
ER -