Minimum Leaf Out-branching and Related Problems

Simple item page
dc.creatorGutin, G.
dc.creatorRazgon, I.
dc.creatorKim, E. J.
dc.date2008-01-13
dc.date2008-10-14
dc.date.accessioned2026-07-07T10:09:17Z
dc.date.available2026-07-07T10:09:17Z
dc.descriptionGiven 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 $O(k^2)$ and construct an algorithm of running time $O(2^{O(k\log k)}+n^6),$ 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.
dc.descriptionThe main change is a quadratic kernel derivation
dc.identifierhttps://arxiv.org/abs/0801.1979
dc.identifierhttp://arxiv.org/abs/0801.1979
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171274
dc.subjectData Structures and Algorithms
dc.subjectDiscrete Mathematics
dc.titleMinimum Leaf Out-branching and Related Problems
dc.typetext

Files

Collections

arXiv