Algorithm for finding k-vertex out-trees and its application to k-internal out-branching problem

Nathann Cohen (1) , Fedor V. Fomin (2) , Gregory Gutin (3) , Eun Jung Kim (3) , Saket Saurabh (4) , Anders Yeo (3)

1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
2 UiB - Department of Informatics [Bergen]
3 Department of Computer Science
4 IMSc - Institute of Mathematical Sciences [Chennai]

An out-tree T is an oriented tree with only one vertex of in-degree zero. A vertex x of T is internal if its out-degree is positive. We design randomized and deterministic algorithms for deciding whether an input digraph contains a given out-tree with k vertices. The algorithms are of running time O*(5.704k) and O*(6.14k), respectively. We apply the deterministic algorithm to obtain a deterministic algorithm of runtime O*(ck), where c is a constant, for deciding whether an input digraph contains a spanning out-tree with at least k internal vertices. This answers in affirmative a question of Gutin, Razgon and Kim (Proc. AAIM'08) [9]

Domaines: Combinatoire [math.CO]; Complexité [cs.CC]

Nathann Cohen, Fedor V. Fomin, Gregory Gutin, Eun Jung Kim, Saket Saurabh, et al.. Algorithm for finding k-vertex out-trees and its application to k-internal out-branching problem. Journal of Computer and System Sciences, 2010, 76 (7), pp.650 - 662. ⟨hal-00504734⟩