# Minimum leaf out-branching problems

Gutin, G. and Razgon, Igor and Kim, E.J.
(2008)
Minimum leaf out-branching problems.
In:
Fleischer, R. and Xu, J. (eds.)
*Algorithmic Aspects in Information and Management.*
Lecture Notes in Computer Science 5034.
Berlin, Germany:
Springer Verlag, pp. 235-246.
ISBN 9783540688808.

## Abstract

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.

## Metadata

Item Type: | Book Section |
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School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |

Depositing User: | Sarah Hall |

Date Deposited: | 01 Aug 2013 15:59 |

Last Modified: | 09 Aug 2023 12:34 |

URI: | https://eprints.bbk.ac.uk/id/eprint/7928 |

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