Algorithm for Finding k-Vertex Out-trees and Its Application to k-Internal Out-branching Problem

  • Nathann Cohen
  • Fedor V. Fomin
  • Gregory Gutin
  • Eun Jung Kim
  • Saket Saurabh
  • Anders Yeo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5609)


An out-treeT is an oriented tree with exactly one vertex of in-degree zero and a vertex x of T is called internal if its out-degree is positive. We design randomized and deterministic algorithms for deciding whether an input digraph contains a subgraph isomorphic to a given out-tree with k vertices. Both algorithms run in O*(5.704k) time. We apply the deterministic algorithm to obtain an algorithm of runtime O*(ck), where c is a constant, for deciding whether an input digraph contains a spanning out-tree with at least k internal vertices. This answers in affirmative a question of Gutin, Razgon and Kim (Proc. AAIM’08).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Nathann Cohen
    • 1
  • Fedor V. Fomin
    • 2
  • Gregory Gutin
    • 3
  • Eun Jung Kim
    • 3
  • Saket Saurabh
    • 2
  • Anders Yeo
    • 3
  1. 1.INRIA – Projet MASCOTTESophia Antipolis CedexFrance
  2. 2.Department of InformaticsUniversity of BergenBergenNorway
  3. 3.Department of Computer Science Royal HollowayUniversity of LondonUK

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