The b-branching problem in digraphs

Naonori Kakimura, Naoyuki Kamiyama, Kenjiro Takazawa

研究成果: Article査読

1 被引用数 (Scopus)

抄録

In this paper, we introduce the concept of b-branchings in digraphs, which is a generalization of branchings serving as a counterpart of b-matchings. Here b is a positive integer vector on the vertex set of a digraph D, and a b-branching is defined as a common independent set of two matroids defined by b: an arc set is a b-branching if it has, for every vertex v of D, at most b(v) arcs entering v, and it is an independent set of a certain sparsity matroid defined by b and D. We demonstrate that b-branchings yield an appropriate generalization of branchings by extending several classic results on branchings. We first present a multi-phase greedy algorithm for finding a maximum-weight b-branching. We then prove a packing theorem extending Edmonds’ disjoint branchings theorem, and provide a strongly polynomial algorithm for finding optimal disjoint b-branchings. As a consequence of the packing theorem, we prove the integer decomposition property of the b-branching polytope. Finally, we deal with a further generalization in which a matroid constraint is imposed on the b(v) arcs sharing the terminal vertex v.

本文言語English
ページ(範囲)565-576
ページ数12
ジャーナルDiscrete Applied Mathematics
283
DOI
出版ステータスPublished - 2020 9 15

ASJC Scopus subject areas

  • 離散数学と組合せ数学
  • 応用数学

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