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.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics