TY - GEN

T1 - Covering directed graphs by in-trees

AU - Kamiyama, Naoyuki

AU - Katoh, Naoki

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2008

Y1 - 2008

N2 - Given a directed graph D = (V,A) with a set of d specified vertices S = {s1,...,s d }⊆ V and a function f: S → ℤ+ where ℤ+ denotes the set of non-negative integers, we consider the problem which asks whether there exist ∑i=1d f (si) in-trees denoted by T i, 1, Ti, 2, ..., Ti f(si) for every i = 1,...,d such that Ti, 1,...,Ti, f(si) are rooted at s i, each Ti,j spans vertices from which s i is reachable and the union of all arc sets of Ti,j for i = 1,...,d and j = 1,...,f(si ) covers A. In this paper, we prove that such set of in-trees covering A can be found by using an algorithm for the weighted matroid intersection problem in time bounded by a polynomial in ∑i=1d f (si) and the size of D. Furthermore, for the case where D is acyclic, we present another characterization of the existence of in-trees covering A, and then we prove that in-trees covering A can be computed more efficiently than the general case by finding maximum matchings in a series of bipartite graphs.

AB - Given a directed graph D = (V,A) with a set of d specified vertices S = {s1,...,s d }⊆ V and a function f: S → ℤ+ where ℤ+ denotes the set of non-negative integers, we consider the problem which asks whether there exist ∑i=1d f (si) in-trees denoted by T i, 1, Ti, 2, ..., Ti f(si) for every i = 1,...,d such that Ti, 1,...,Ti, f(si) are rooted at s i, each Ti,j spans vertices from which s i is reachable and the union of all arc sets of Ti,j for i = 1,...,d and j = 1,...,f(si ) covers A. In this paper, we prove that such set of in-trees covering A can be found by using an algorithm for the weighted matroid intersection problem in time bounded by a polynomial in ∑i=1d f (si) and the size of D. Furthermore, for the case where D is acyclic, we present another characterization of the existence of in-trees covering A, and then we prove that in-trees covering A can be computed more efficiently than the general case by finding maximum matchings in a series of bipartite graphs.

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U2 - 10.1007/978-3-540-69733-6_44

DO - 10.1007/978-3-540-69733-6_44

M3 - Conference contribution

AN - SCOPUS:48249139377

SN - 3540697322

SN - 9783540697329

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 444

EP - 457

BT - Computing and Combinatorics - 14th Annual International Conference, COCOON 2008, Proceedings

T2 - 14th Annual International Conference on Computing and Combinatorics, COCOON 2008

Y2 - 27 June 2008 through 29 June 2008

ER -