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

Authors:
Nathann Cohen;Fedor V. Fomin;Gregory Gutin;Eun Jung Kim;Saket Saurabh;Anders Yeo
Affiliations:
INRIA -- Projet MASCOTTE, 2004 route des Lucioles, BP 93 F-06902, Sophia Antipolis Cedex, France;Department of Informatics, University of Bergen, POB 7803, 5020 Bergen, Norway;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK;Department of Informatics, University of Bergen, POB 7803, 5020 Bergen, Norway;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK
Venue:
Journal of Computer and System Sciences
Year:
2010

Citing 7
Cited 3

Storing a Sparse Table with 0(1) Worst Case Access Time

Journal of the ACM (JACM)
Color-coding

Journal of the ACM (JACM)
Splitters and near-optimal derandomization

FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Reducing to independent set structure: the case of k-internal spanning tree

Nordic Journal of Computing
Faster Algebraic Algorithms for Path and Packing Problems

ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Finding paths of length k in O∗(2k) time

Information Processing Letters
Digraphs: Theory, Algorithms and Applications

Digraphs: Theory, Algorithms and Applications

Faster algorithms for finding and counting subgraphs

Journal of Computer and System Sciences
A linear vertex kernel for maximum internal spanning tree

Journal of Computer and System Sciences
Beyond bidimensionality: Parameterized subexponential algorithms on directed graphs

Information and Computation

Quantified Score

Hi-index	0.01

Visualization

Abstract

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^*(5.704^k) and O^*(6.14^k), 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) [9].