Using Interior-Point Methods for Fast Parallel Algorithms for Bipartite Matching and Related Problems

In this paper we use interior-point methods for linear programming, developed in the context of sequential computation, to obtain a parallel algorithm for the bipartite matching problem. Our algorithm nds a maximum cardinality matching in a bipartite graph with n nodes and m edges in O(pm log3 n) time on a CRCW PRAM. Our results extend to the weighted bipartite matching problem and to the zero-one minimum-cost ow problem, yieldingO(pm log2 n lognC) algorithms, where C > 1 is an upper bound on the absolute value of the integral weights or costs in the two problems, respectively. Our results improve previous bounds on these problems and introduce interior-point methods to the context of parallel algorithm design.