Arc-disjoint in-trees in directed graphs

Naoyuki Kamiyama, Naoki Katoh, Atsushi Takizawa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationProceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms
Pages518-526
Number of pages9
Publication statusPublished - Dec 1 2008
Externally publishedYes
Event19th Annual ACM-SIAM Symposium on Discrete Algorithms - San Francisco, CA, United States
Duration: Jan 20 2008Jan 22 2008

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

Other19th Annual ACM-SIAM Symposium on Discrete Algorithms
CountryUnited States
CitySan Francisco, CA
Period1/20/081/22/08

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All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

Cite this

Kamiyama, N., Katoh, N., & Takizawa, A. (2008). Arc-disjoint in-trees in directed graphs. In Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 518-526). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).