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, Sophia Antipolis Cedex, France F-06902;Department of Informatics, University of Bergen, Bergen, Norway POB 7803, 5020;Department of Computer Science Royal Holloway, University of London, UK TW20 0EX;Department of Computer Science Royal Holloway, University of London, UK TW20 0EX;Department of Informatics, University of Bergen, Bergen, Norway POB 7803, 5020;Department of Computer Science Royal Holloway, University of London, UK TW20 0EX
Venue:
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Year:
2009

Citing 9
Cited 2

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
Improved algorithms for path, matching, and packing problems

SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Minimum Leaf Out-Branching Problems

AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
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
Divide-and-color

WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science

A Linear Vertex Kernel for Maximum Internal Spanning Tree

ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Sharp separation and applications to exact and parameterized algorithms

LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics

Quantified Score

Hi-index	0.00

Visualization

Abstract

An out-tree T is an oriented tree with exactly one vertex of in-degree zero and a vertex x of T is called internal if its out-degree is positive. We design randomized and deterministic algorithms for deciding whether an input digraph contains a subgraph isomorphic to a given out-tree with k vertices. Both algorithms run in O *(5.704 k ) time. We apply the deterministic algorithm to obtain an 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).