PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Algorithm for Finding $k$-Vertex Out-trees and its Application to $k$-Internal Out-branching Problem.
N. Cohen, F. Fomin, Gregory Gutin, E.J. Kim, S. Saurabh and A. Yeo
COCOON'09 2009.


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 runtime $O^*(5.704^k)$ and $O^*(5.704^{k(1+o(1))})$, respectively. We apply the deterministic algorithm to obtain a deterministic algorithm of runtime $O^*(c^k)$, 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).

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:5190
Deposited By:Gregory Gutin
Deposited On:24 March 2009