Abstract
In this study we consider the Minimum Cost Bipartite Perfect Matching Problem with Conflict Pair Constraints (MCBPMPC) on bipartite graphs. Given a bipartite graph G with a cost associated with each edge and a conflict set of edge pairs, the MCBPMPC consists of finding a perfect matching with the lowest total cost such that no more than one edge is selected from each pair in the conflict set. A specially tailored branch-and-bound (B&B) algorithm is introduced. Computational experiments are performed on randomly generated instances. According to the extensive experiments, the suggested B&B algorithm yields promising results compared to a state-of-the-art mixed integer linear programming solver.
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