We consider the problem of matching applicants to posts where applicants have preferences over posts. Thus the input to our problem is a bipartite graph (formula presented), where \mathcal {A} denotes a set of applicants, \mathcal {P} is a set of posts, and there are ranks on edges which denote the preferences of applicants over posts. A matching M in G is called rank-maximal if it matches the maximum number of applicants to their rank in a dynamic setting, where vertices and edges can be added and deleted at any point. Let n and m be the number of vertices and edges in an instance G, and r be the maximum rank used by any rank-maximal matching in G. We give a simple O(r(m+n)) -time algorithm to update an existing rank-maximal matching under each of these changes. When r=o(n), this is faster than recomputing a rank-maximal matching completely using a known algorithm like that of Irving et al. [13], which takes time (formula presented).
CITATION STYLE
Nimbhorkar, P., & Arvind Rameshwar, A. (2017). Dynamic rank-maximal matchings. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10392 LNCS, pp. 433–444). Springer Verlag. https://doi.org/10.1007/978-3-319-62389-4_36
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