Semi-matchings for bipartite graphs and load balancing

We consider the problem of fairly matching the left-hand vertices of a bipartite graph to the right-hand vertices. We refer to this problem as the optimal semimatching problem; it is a relaxation of the known bipartite matching problem. We present a way to evaluate the quality of a given semi-matching and show that, under this measure, an optimal semi-matching balances the load on the right hand vertices with respect to any Lp-norm. In particular, when modeling a job assignment system, an optimal semi-matching achieves the minimal makespan and the minimal flow time for the system. The problem of finding optimal semi-matchings is a special case of certain scheduling problems for which known solutions exist. However, these known solutions are based on general network optimization algorithms, and are not the most efficient way to solve the optimal semi-matching problem. To compute optimal semi-matchings efficiently, we present and analyze two new algorithms. The first algorithm generaliz...

• Type: Journal
• Year: 2006
• Where: JAL
• Authors: Nicholas J. A. Harvey, Richard E. Ladner, László Lovász, Tami Tamir
• Keywords: Algorithms, Bipartite Matchings, JAL 2006, Optimal Semi-matching