Reconfiguration of maximum-weight b-matchings in a graph

Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto

研究成果: Conference contribution

3 被引用数 (Scopus)

抄録

Consider a graph such that each vertex has a nonnegative integer capacity and each edge has a positive integer weight. Then, a b-matching in the graph is a multi-set of edges (represented by an integer vector on edges) such that the total number of edges incident to each vertex is at most the capacity of the vertex. In this paper, we study a reconfiguration variant for maximum-weight b-matchings: For two given maximum-weight b-matchings in a graph, we are asked to determine whether there exists a sequence of maximum-weight b-matchings in the graph between them, with subsequent b-matchings obtained by removing one edge and adding another. We show that this reconfiguration problem is solvable in polynomial time for instances with no integrality gap. Such instances include bipartite graphs with any capacity function on vertices, and 2-matchings in general graphs. Thus, our result implies that the reconfiguration problem for maximum-weight matchings can be solved in polynomial time for bipartite graphs.

本文言語English
ホスト出版物のタイトルComputing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings
編集者Yixin Cao, Jianer Chen
出版社Springer Verlag
ページ287-296
ページ数10
ISBN(印刷版)9783319623887
DOI
出版ステータスPublished - 2017
イベント23rd International Conference on Computing and Combinatorics, COCOON 2017 - Hong Kong, China
継続期間: 2017 8 32017 8 5

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
10392 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Other

Other23rd International Conference on Computing and Combinatorics, COCOON 2017
国/地域China
CityHong Kong
Period17/8/317/8/5

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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