Minimum Leaf Out-Branching Problems

  • Gregory Gutin
  • Igor Razgon
  • Eun Jung Kim
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5034)


Given a digraph D, the Minimum Leaf Out-Branching problem (MinLOB) is the problem of finding in D an out-branching with the minimum possible number of leaves, i.e., vertices of out-degree 0. We prove that MinLOB is polynomial-time solvable for acyclic digraphs. In general, MinLOB is NP-hard and we consider three parameterizations of MinLOB. We prove that two of them are NP-complete for every value of the parameter, but the third one is fixed-parameter tractable (FPT). The FPT parametrization is as follows: given a digraph D of order n and a positive integral parameter k, check whether D contains an out-branching with at most n − k leaves (and find such an out-branching if it exists). We find a problem kernel of order O(k·2 k ) and construct an algorithm of running time O(2 O(klogk) + n 3), which is an ‘additive’ FPT algorithm.


Bipartite Graph Vertex Cover Tree Decomposition Acyclic Digraph Problem Kernel 
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 2008

Authors and Affiliations

  • Gregory Gutin
    • 1
  • Igor Razgon
    • 2
  • Eun Jung Kim
    • 1
  1. 1.Department of Computer Science Royal HollowayUniversity of London, Egham, SurreyUK
  2. 2.Department of Computer ScienceUniversity College CorkIreland

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