Gutin, G. and Razgon, Igor and Kim, E.J. (2009) Minimum leaf out-branching and related problems. Theoretical Computer Science 410 (45), pp. 4571-4579. ISSN 0304-3975.
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 parameterization 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(k2) and construct an algorithm of running time O(2O(klogk)+n6), which is an ‘additive’ FPT algorithm. We also consider transformations from two related problems, the minimum path covering and the maximum internal out-tree problems into MinLOB, which imply that some parameterizations of the two problems are FPT as well.
Metadata
| Item Type: | Article |
|---|---|
| Keyword(s) / Subject(s): | directed graphs, out-branchings, minimum number of leaves, fixed-parameter tractable, acyclic directed graphs |
| School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Sarah Hall |
| Date Deposited: | 01 Aug 2013 15:54 |
| Last Modified: | 09 Aug 2023 12:34 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/7927 |
Statistics
Additional statistics are available via IRStats2.
Archive Staff Only (login required)
