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-tree T 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 *(5.704 k ) time. We apply the deterministic algorithm to obtain an algorithm of runtime O *(c k ), 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).


Rooted Tree Deterministic Algorithm Recursive Call Internal Vertex Oriented Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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