Reconfiguration of maximum-weight b-matchings in a graph

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

doi:10.1007/978-3-319-62389-4_24

Reconfiguration of maximum-weight b-matchings in a graph

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

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

3 Citations (Scopus)

Abstract

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.

Original language	English
Title of host publication	Computing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings
Publisher	Springer Verlag
Pages	287-296
Number of pages	10
Volume	10392 LNCS
ISBN (Print)	9783319623887
DOIs	https://doi.org/10.1007/978-3-319-62389-4_24
Publication status	Published - 2017
Event	23rd International Conference on Computing and Combinatorics, COCOON 2017 - Hong Kong, China Duration: 2017 Aug 3 → 2017 Aug 5

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10392 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	23rd International Conference on Computing and Combinatorics, COCOON 2017
Country	China
City	Hong Kong
Period	17/8/3 → 17/8/5

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-319-62389-4_24

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Cite this

Ito, T., Kakimura, N., Kamiyama, N., Kobayashi, Y., & Okamoto, Y. (2017). Reconfiguration of maximum-weight b-matchings in a graph. In Computing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings (Vol. 10392 LNCS, pp. 287-296). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 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. Vol. 10392 LNCS Springer Verlag, 2017. p. 287-296 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10392 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Ito, T, Kakimura, N, Kamiyama, N, Kobayashi, Y & Okamoto, Y 2017, Reconfiguration of maximum-weight b-matchings in a graph. in Computing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings. vol. 10392 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10392 LNCS, Springer Verlag, pp. 287-296, 23rd International Conference on Computing and Combinatorics, COCOON 2017, Hong Kong, China, 17/8/3. 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. In Computing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings. Vol. 10392 LNCS. 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. Vol. 10392 LNCS 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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