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Algorithms for finding a Kth best valued assignment |
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| Authors: | Tomomi Matsui Akihisa Tamura Yoshiko Ikebe |
| Affiliation: | a Department of Industrial Administration, Science University of Tokyo, Noda, Chiba 278, Japan b Department of Information Sciences, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152, Japan |
| Abstract: | We consider a new problem, the Kth best valued assignment problem. Given a bipartite graph G and a cost vector w on its edge set, this is the problem of finding a perfect matching Mk in G such that there exist perfect matchings M1,…,MK−1 satisfying w(M1) < < w(MK−1) < w(MK), and w(MK) < w(M) for all perfect matchings M with w(M) ≠ w(M1),…,w(MK). Here w(M) denotes the sum of costs of edges in M. In this paper, we propose two algorithms for solving this problem and verify the efficiency of our algorithms by our preliminary computational experiments. |
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