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Information Processing Letters
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ACM SIGACT News
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Theory of Computing Systems
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Algorithmica - Parameterized and Exact Algorithms
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Digraphs: Theory, Algorithms and Applications
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FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Parameterized algorithms for directed maximum leaf problems
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Parameterized Complexity
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ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Algorithm for Finding k-Vertex Out-trees and Its Application to k-Internal Out-branching Problem
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Tight bounds and a fast FPT algorithm for directed Max-Leaf Spanning Tree
ACM Transactions on Algorithms (TALG)
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LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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Mathematical and Computer Modelling: An International Journal
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Discrete Optimization
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Given a digraph D, the Minimum Leaf Out-Branching problem (MinLOB) is the problem of finding in Dan 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 Dof order nand a positive integral parameter k, check whether Dcontains an out-branching with at most n驴 kleaves (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(klogk)+ n3), which is an `additive' FPT algorithm.