Minimum Leaf Out-Branching Problems

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Minimum Leaf Out-Branching Problems
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 outbranching with at most n − k leaves (and find such an out-branching if it exists). We find a problem kernel of order O(k · 2k ) and construct an algorithm of running time O(2O(k log k) + n3 ), which is an ‘additive’ FPT algorithm.
Gregory Gutin, Igor Razgon, Eun Jung Kim
Added 01 Jun 2010
Updated 01 Jun 2010
Type Conference
Year 2008
Where AAIM
Authors Gregory Gutin, Igor Razgon, Eun Jung Kim
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