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Rank-Maximal Matchings

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45021

Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45040

Michail,  Dimitrios
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45155

Paluch,  Katarzyna
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Zitation

Irving, R. W., Kavitha, T., Mehlhorn, K., Michail, D., & Paluch, K. (2006). Rank-Maximal Matchings. ACM Transactions on Algorithms, 2, 602-610.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-23C5-9
Zusammenfassung
Suppose that each member of a set A of applicants ranks a subset of a set P of posts in an order of preference, possibly involving ties. A matching is a set of (applicant, post) pairs such that each applicant and each post appears in at most one pair. A rank-maximal matching is one in which the maximum possible number of applicants are matched to their first choice post, and subject to that condition, the maximum possible number are matched to their second choice post, and so on. This is a relevant concept in any practical matching situation and it was first studied by Irving [2003].We give an algorithm to compute a rank-maximal matching with running time O(min(n + C,C√n)m), where C is the maximal rank of an edge used in a rank-maximal matching, n is the number of applicants and posts and m is the total size of the preference lists.