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    Minimum leaf out-branching and related problems

    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.

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    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.


    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


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