TY - GEN
T1 - Representative families
T2 - 22nd Annual European Symposium on Algorithms, ESA 2014
AU - Shachnai, Hadas
AU - Zehavi, Meirav
PY - 2014/1/1
Y1 - 2014/1/1
N2 - Let M = (E, I)be a matroid, and let S be a family of subsets of size p of E. A subfamily Ŝ⊆S represents if for every pair of sets X ε S and Y ⊆ E \X such that X ∪ Y ε I, there is a set X̂ε Ŝ disjoint from Y such that X̂ ∪ Y ε I.. Fomin et al. (Proc. ACM-SIAM Symposium on Discrete Algorithms, 2014) introduced a powerful technique for fast computation of representative families for uniform matroids. In this paper, we show that this technique leads to a unified approach for substantially improving the running times of parameterized algorithms for some classic problems. This includes, among others, k -Partial Cover, k -Internal Out-Branching, and Long Directed Cycle. Our approach exploits an interesting tradeoff between running time and the size of the representative families.
AB - Let M = (E, I)be a matroid, and let S be a family of subsets of size p of E. A subfamily Ŝ⊆S represents if for every pair of sets X ε S and Y ⊆ E \X such that X ∪ Y ε I, there is a set X̂ε Ŝ disjoint from Y such that X̂ ∪ Y ε I.. Fomin et al. (Proc. ACM-SIAM Symposium on Discrete Algorithms, 2014) introduced a powerful technique for fast computation of representative families for uniform matroids. In this paper, we show that this technique leads to a unified approach for substantially improving the running times of parameterized algorithms for some classic problems. This includes, among others, k -Partial Cover, k -Internal Out-Branching, and Long Directed Cycle. Our approach exploits an interesting tradeoff between running time and the size of the representative families.
UR - http://www.scopus.com/inward/record.url?scp=84958526789&partnerID=8YFLogxK
U2 - 10.1007/978-3-662-44777-2_65
DO - 10.1007/978-3-662-44777-2_65
M3 - Conference contribution
AN - SCOPUS:84958526789
SN - 9783662447765
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 786
EP - 797
BT - Algorithms, ESA 2014 - 22nd Annual European Symposium, Proceedings
PB - Springer Verlag
Y2 - 8 September 2014 through 10 September 2014
ER -