The B-branching problem in digraphs

Naonori Kakimura, Naoyuki Kamiyama, Kenjiro Takazawa

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

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Title of host publication43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018
EditorsIgor Potapov, James Worrell, Paul Spirakis
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Volume117
ISBN (Print)9783959770866
DOIs
Publication statusPublished - 2018 Aug 1
Event43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018 - Liverpool, United Kingdom
Duration: 2018 Aug 272018 Aug 31

Other

Other43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018
CountryUnited Kingdom
CityLiverpool
Period18/8/2718/8/31

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Keywords

  • Arborescence
  • Greedy algorithm
  • Matroid intersection
  • Packing
  • Sparsity matroid

ASJC Scopus subject areas

  • Software

Cite this

Kakimura, N., Kamiyama, N., & Takazawa, K. (2018). The B-branching problem in digraphs. In I. Potapov, J. Worrell, & P. Spirakis (Eds.), 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018 (Vol. 117). [12] Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.MFCS.2018.12