TY - GEN

T1 - Reconfiguration of maximum-weight b-matchings in a graph

AU - Ito, Takehiro

AU - Kakimura, Naonori

AU - Kamiyama, Naoyuki

AU - Kobayashi, Yusuke

AU - Okamoto, Yoshio

N1 - Funding Information:
T. Ito – Supported by JST CREST Grant Number JPMJCR1402, Japan, and JSPS KAKENHI Grant Number JP16K00004. N. Kakimura – Supported by JST ERATO Grant Number JPMJER1305, Japan, and by JSPS KAKENHI Grant Number JP17K00028. N. Kamiyama – Supported by JST PRESTO Grant Number JPMJPR14E1, Japan. Y. Kobayashi – Supported by JST ERATO Grant Number JPMJER1305, Japan, and by JSPS KAKENHI Grant Numbers JP16K16010 and JP16H03118. Y. Okamoto – Supported by Kayamori Foundation of Informational Science Advancement, JST CREST Grant Number JPMJCR1402, Japan, and JSPS KAK-ENHI Grant Numbers JP24106005, JP24700008, JP24220003, JP15K00009.
Publisher Copyright:
© 2017, Springer International Publishing AG.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-319-62389-4_24

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

M3 - Conference contribution

AN - SCOPUS:85028448554

SN - 9783319623887

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 287

EP - 296

BT - Computing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings

A2 - Cao, Yixin

A2 - Chen, Jianer

PB - Springer Verlag

T2 - 23rd International Conference on Computing and Combinatorics, COCOON 2017

Y2 - 2 August 2017 through 4 August 2017

ER -