Reconfiguration of maximum-weight b-matchings in a graph

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

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
Title of host publicationComputing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings
EditorsYixin Cao, Jianer Chen
PublisherSpringer Verlag
Pages287-296
Number of pages10
ISBN (Print)9783319623887
DOIs
Publication statusPublished - Jan 1 2017
Event23rd International Conference on Computing and Combinatorics, COCOON 2017 - Hong Kong, China
Duration: Aug 3 2017Aug 5 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10392 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other23rd International Conference on Computing and Combinatorics, COCOON 2017
CountryChina
CityHong Kong
Period8/3/178/5/17

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)

Cite this

Ito, T., Kakimura, N., Kamiyama, N., Kobayashi, Y., & Okamoto, Y. (2017). Reconfiguration of maximum-weight b-matchings in a graph. In Y. Cao, & J. Chen (Eds.), 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); 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. ed. / 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); Vol. 10392 LNCS).

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

Ito, T, Kakimura, N, Kamiyama, N, Kobayashi, Y & Okamoto, Y 2017, Reconfiguration of maximum-weight b-matchings in a graph. in Y Cao & J Chen (eds), 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), vol. 10392 LNCS, Springer Verlag, pp. 287-296, 23rd International Conference on Computing and Combinatorics, COCOON 2017, Hong Kong, China, 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. In Cao Y, Chen J, editors, 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. editor / 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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