Faster scaling algorithms for network problems
SIAM Journal on Computing
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
An efficient cost scaling algorithm for the assignment problem
Mathematical Programming: Series A and B
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
A Decomposition Theorem for Maximum Weight Bipartite Matchings
SIAM Journal on Computing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
ACM Transactions on Algorithms (TALG)
Pareto optimality in house allocation problems
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
An experimental comparison of single-sided preference matching algorithms
Journal of Experimental Algorithmics (JEA)
| Hi-index | 5.23 |
Given a bipartite graph G(V,E), V=A@?@?B where |V|=n,|E|=m and a partition of the edge set into r@?m disjoint subsets E=E"1@?@?E"2@?@?...@?@?E"r, which are called ranks, the rank-maximal matching problem is to find a matching M of G such that |M@?E"1| is maximized and given that |M@?E"1| is maximized, |M@?E"2| is also maximized, and so on. Such a problem arises as an optimization criteria over a possible assignment of a set of applicants to a set of posts. The matching represents the assignment and the ranks on the edges correspond to a ranking of the posts submitted by the applicants. The rank-maximal matching problem and several other optimization variants, e.g. fair matching and maximum cardinality rank-maximal matching, can be solved by a reduction to the weight matching problem in time O(rnmlogn). Recently, Irving et al. developed a combinatorial approach which improves the running time for the rank-maximal matching problem to O(min(n+r,rn)m). They raised the open questions on (a) whether such a running time can be achieved by the weight matching reduction and (b) whether such a running time can be achieved for the other variants of the problem. In this work we show how the reduction to the weight matching problem can also be used to achieve the same running time. Our algorithm is simpler and more intuitive.