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- W2155539817 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 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." @default.
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- W2155539817 date "2009-07-01" @default.
- W2155539817 modified "2023-09-30" @default.
- W2155539817 title "On complexity of Minimum Leaf Out-Branching problem" @default.
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- W2155539817 doi "https://doi.org/10.1016/j.dam.2009.04.012" @default.
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