The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Faster scaling algorithms for network problems
SIAM Journal on Computing
Handbook of combinatorics (vol. 1)
Strong Stability in the Hospitals/Residents Problem
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Reducing rank-maximal to maximum weight matching
Theoretical Computer Science
Note: Optimal popular matchings
Discrete Applied Mathematics
Popular Matchings: Structure and Algorithms
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
A fair assignment algorithm for multiple preference queries
Proceedings of the VLDB Endowment
Popular Matchings with Variable Job Capacities
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Popular matchings in the weighted capacitated house allocation problem
Journal of Discrete Algorithms
The stable roommates problem with globally-ranked pairs
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Popular matchings with variable item copies
Theoretical Computer Science
An experimental comparison of single-sided preference matching algorithms
Journal of Experimental Algorithmics (JEA)
ACM Transactions on Algorithms (TALG)
Matching with sizes (or scheduling with processing set restrictions)
Discrete Applied Mathematics
Journal of Combinatorial Optimization
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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 &sqrt;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.