Reconfiguration of maximum-weight b-matchings in a graph

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

研究成果: 著書/レポートタイプへの貢献会議での発言

3 引用 (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.

元の言語英語
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
出版者Springer Verlag
ページ287-296
ページ数10
ISBN(印刷物)9783319623887
DOI
出版物ステータス出版済み - 1 1 2017
イベント23rd International Conference on Computing and Combinatorics, COCOON 2017 - Hong Kong, 中国
継続期間: 8 3 20178 5 2017

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(印刷物)0302-9743
ISSN(電子版)1611-3349

その他

その他23rd International Conference on Computing and Combinatorics, COCOON 2017
中国
Hong Kong
期間8/3/178/5/17

Fingerprint

Reconfiguration
Polynomials
Graph in graph theory
Bipartite Graph
Integer
Polynomial time
Vertex of a graph
Integrality
Multiset
Non-negative
Imply

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

これを引用

Ito, T., Kakimura, N., Kamiyama, N., Kobayashi, Y., & Okamoto, Y. (2017). Reconfiguration of maximum-weight b-matchings in a graph. : Y. Cao, & J. Chen (版), Computing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings (pp. 287-296). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 10392 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-62389-4_24

Reconfiguration of maximum-weight b-matchings in a graph. / Ito, Takehiro; Kakimura, Naonori; Kamiyama, Naoyuki; Kobayashi, Yusuke; Okamoto, Yoshio.

Computing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings. 版 / Yixin Cao; Jianer Chen. Springer Verlag, 2017. p. 287-296 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻 10392 LNCS).

研究成果: 著書/レポートタイプへの貢献会議での発言

Ito, T, Kakimura, N, Kamiyama, N, Kobayashi, Y & Okamoto, Y 2017, Reconfiguration of maximum-weight b-matchings in a graph. : Y Cao & J Chen (版), Computing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 巻. 10392 LNCS, Springer Verlag, pp. 287-296, 23rd International Conference on Computing and Combinatorics, COCOON 2017, Hong Kong, 中国, 8/3/17. https://doi.org/10.1007/978-3-319-62389-4_24
Ito T, Kakimura N, Kamiyama N, Kobayashi Y, Okamoto Y. Reconfiguration of maximum-weight b-matchings in a graph. : Cao Y, Chen J, 編集者, Computing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings. Springer Verlag. 2017. p. 287-296. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-62389-4_24
Ito, Takehiro ; Kakimura, Naonori ; Kamiyama, Naoyuki ; Kobayashi, Yusuke ; Okamoto, Yoshio. / Reconfiguration of maximum-weight b-matchings in a graph. Computing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings. 編集者 / Yixin Cao ; Jianer Chen. Springer Verlag, 2017. pp. 287-296 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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