Algorithms for finding a Kth best valued assignment

Tomomi Matsui; Akihisa Tamura; Yoshiko Ikebe

doi:10.1016/0166-218X(92)00175-L

Algorithms for finding a Kth best valued assignment

Tomomi Matsui, Akihisa Tamura, Yoshiko Ikebe

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 M_k in G such that there exist perfect matchings M₁,...,M_K-1 satisfying w(M₁) < ⋯ < w(M_K-1) < w(M_K), and w(M_K) < w(M) for all perfect matchings M with w(M) ≠ w(M₁),...,w(M_K). 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.

Original language	English
Pages (from-to)	283-296
Number of pages	14
Journal	Discrete Applied Mathematics
Volume	50
Issue number	3
DOIs	https://doi.org/10.1016/0166-218X(92)00175-L
Publication status	Published - 1994 May 20
Externally published	Yes

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/0166-218X(92)00175-L

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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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AU - Matsui, Tomomi

AU - Tamura, Akihisa

AU - Ikebe, Yoshiko

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N2 - 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.

AB - 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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Algorithms for finding a Kth best valued assignment

Abstract

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