Kibern. vyčisl. teh., 2018, Issue 1 (191), pp.
Kyyko V.M., PhD (Engineering),
Senior Researcher of Pattern Recognition Department
International Research and Training Center
for Information Technologies and Systems
of the National Academy of Sciences of Ukraine
and Ministry of Education and Science of Ukraine,
Acad. Glushkov av., 40, Kiev, 03187, Ukraine
MAXIMUM MATCHING IN WEIGHTED BIPARTITE GRAPHS
Introduction. The most important algorithms for bipartite graphs maximum matching are observed. These algorithms either find maximum matching in non-weighted bipartite graph (e.g. Hopcroft and Karp’s algorithm — ) or choose among all matchings with maximum size one having maximal cost (e.g. Edmonds and Karp’s algorithm-). Provided that, in praxis new target settings and algorithms for finding maximum matching in bipartite graphs are also desirable.
The purpose of the article is to consider a new task setting and algorithms for maximum matching in weighted bipartite graphs as well as using these algorithms in fingerprint recognition.
Methods. Modified versions of finding maximum matching M in graph by searching and augmentation of M-augmenting paths are used.
Results. Weighted bipartite graph with a cost function , that associates each edge with one of two possible values (e.g. 0 or 1) is considered. Maximum matching in the graph in new setting consists in finding among all matchings containing maximum number of edges with weight 1, one having maximal cardinality. Two algorithms with complexity being modified versions of the Hopcroft-Karp algorithm are proposed. Examples of using these algorithms for removing gaps of lines and finding true correspondence of minutiae in fingerprint recognition are considered.
Conclusions. Proposed algorithms find maximum matching in input bipartite graph among all matchings having maximal cardinality in given subset of this graph edges. Using of proposed algorithms leads to increasing processing speed and reliability of fingerprint recognition.
Key words: maximum matching, bipartite graph, images
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