The B-branching problem in digraphs

Naonori Kakimura, Naoyuki Kamiyama, Kenjiro Takazawa

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

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, 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 at most b(v) arcs sharing the terminal vertex v, and it is an independent set of a certain sparsity matroid defined by b. We demonstrate that b-branchings yield an appropriate generalization of branchings by extending several classical 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 bbranching 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.

本文言語英語
ホスト出版物のタイトル43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018
編集者Igor Potapov, James Worrell, Paul Spirakis
出版社Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN(印刷版)9783959770866
DOI
出版ステータス出版済み - 8 1 2018
イベント43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018 - Liverpool, 英国
継続期間: 8 27 20188 31 2018

出版物シリーズ

名前Leibniz International Proceedings in Informatics, LIPIcs
117
ISSN(印刷版)1868-8969

その他

その他43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018
Country英国
CityLiverpool
Period8/27/188/31/18

All Science Journal Classification (ASJC) codes

  • Software

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