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Finding all minimum‐cost perfect matchings in Bipartite graphs
Author(s) -
Fukuda Komei,
Matsui Tomomi
Publication year - 1992
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230220504
Subject(s) - bipartite graph , matching (statistics) , enumeration , combinatorics , mathematics , strong perfect graph theorem , graph , algorithm , 3 dimensional matching , computer science , discrete mathematics , line graph , pathwidth , statistics
The Hungarian method is an efficient algorithm for finding a minimal‐cost perfect matching in a weighted bipartite graph. This paper describes an efficient algorithm for finding all minimal‐cost perfect matchings. The computational time required to generate each additional perfect matching is O ( n ( n + m )), and it requires O ( n + m ) memory storage. This problem can be solved by algorithms for finding the K th‐best solution of assignment problems. However, the memory storage required by the known algorithms grows in proportion to K , and, hence, it may grow exponentially in n . So, our specialized algorithm has a considerable advantage in memory requirement over the precious more general algorithms for K th‐best assignment problems. Here we will show that the enumeration of all minimal‐cost perfect matchings can be reduced to the enumeration of all perfect matchings in some bipartite graph. Therefore, our algorithm can be seen as an algorithm for enumerating all perfect matchings in a given bipartite graph.