On complexity of Minimum Leaf Out-Branching problem

Peter Dankelmann, Gregory Gutin, Eun Jung Kim

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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 zero. Gutin, Razgon and Kim [G. Gutin, I. Razgon, E.J. Kim, Minimum leaf out-branching problems, in: Proc. 4th International Conference on Algorithmic Aspects in Information and Management, AAIM'08, in: Lect. Notes Comput. Sci., vol. 5034 2008, pp. 235-246] proved that MinLOB is polynomial time solvable for acyclic digraphs which are exactly the digraphs of directed path-width (DAG-width, directed tree-width, respectively) 0. We investigate how much one can extend this polynomiality result. We prove that already for digraphs of directed path-width (directed tree-width, DAG-width, respectively) 1, MinLOB is NP-hard. On the other hand, we show that for digraphs of restricted directed tree-width (directed path-width, DAG-width, respectively) and a fixed integer k, the problem of checking whether there is an out-branching with at most k leaves is polynomial time solvable.

Original languageEnglish
Pages (from-to)3000-3004
Number of pages5
JournalDiscrete Applied Mathematics
Issue number13
Publication statusPublished - 6 Jul 2009
Externally publishedYes


  • Computational complexity
  • DAG-width
  • Directed tree-width
  • Leaves
  • Out-branchings

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


Dive into the research topics of 'On complexity of Minimum Leaf Out-Branching problem'. Together they form a unique fingerprint.

Cite this