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Perfect Matching Essential Edges in Balanced Bipartite Graphs by Edge Augmentation

Yueping Li, Renfeng Xu, Zhe Nie

Abstract


Perfect matching in balanced bipartite graphs can represent that all the jobs are distributed to processing machines. This paper presents the concept of "perfect matching essential edge" to characterize the edge lies in every perfect matching. If any perfect matching essential edge fails, the graphs bears no perfect matching; that is, certain job cannot be assigned to any processing machine. This paper discusses the problem of augmenting one balanced bipartite graph to contain no perfect matching essential edge by adding least edges. This problem helps to design robust job assignment circuit. We prove this problem is NP-Complete. Thus, we employ one greedy algorithm of "Minimal Set Cover" problem to solve this problem. Experiment results show our algorithm can improve the number of augmenting edges significantly compared with the best algorithm existed.

Keywords


job assignment, perfect matching, edge augmentation, NP-complete.

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