Representative families: A unified tradeoff-based approach

Hadas Shachnai, Meirav Zehavi

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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 languageEnglish
Pages (from-to)488-502
Number of pages15
JournalJournal of Computer and System Sciences
Issue number3
StatePublished - 1 Jan 2016
Externally publishedYes


  • 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


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