TY - GEN

T1 - Arc-disjoint in-trees in directed graphs

AU - Kamiyama, Naoyuki

AU - Katoh, Naoki

AU - Takizawa, Atsushi

PY - 2008/12/1

Y1 - 2008/12/1

N2 - Given a directed graph D = (V, A) and a set of specified vertices S = {s1,... , Sd} ⊆ V with |S| = d and a function f: S → ℕ where ℕ denotes the set of natural numbers, we present a necessary and sufficient condition that there exist Σsi∈S f(si) arc-disjoint in-trees denoted by Ti,1,T i,2,...,Ti,f(si) for every i = 1,...,d such that Ti,1,..., Ti,f(si) are rooted at s i and each Ti,j spans vertices from which si is reachable. This generalizes the result of Edmonds [2], i.e., the necessary and sufficient condition that for a directed graph D = (V, A) with a specified vertex s ∈ V, there are k arc-disjoint in-trees rooted at s each of which spans V. Furthermore, we extend another characterization of packing in-trees of Edmonds [1] to the one in our case.

AB - Given a directed graph D = (V, A) and a set of specified vertices S = {s1,... , Sd} ⊆ V with |S| = d and a function f: S → ℕ where ℕ denotes the set of natural numbers, we present a necessary and sufficient condition that there exist Σsi∈S f(si) arc-disjoint in-trees denoted by Ti,1,T i,2,...,Ti,f(si) for every i = 1,...,d such that Ti,1,..., Ti,f(si) are rooted at s i and each Ti,j spans vertices from which si is reachable. This generalizes the result of Edmonds [2], i.e., the necessary and sufficient condition that for a directed graph D = (V, A) with a specified vertex s ∈ V, there are k arc-disjoint in-trees rooted at s each of which spans V. Furthermore, we extend another characterization of packing in-trees of Edmonds [1] to the one in our case.

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M3 - Conference contribution

AN - SCOPUS:48249147916

SN - 9780898716474

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 518

EP - 526

BT - Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms

T2 - 19th Annual ACM-SIAM Symposium on Discrete Algorithms

Y2 - 20 January 2008 through 22 January 2008

ER -