An Improved Boolean Circuit for Maximum Matching in a Convex Bipartite Graph

Abstract

The Boolean circuit is a simple and realistic model for parallel computation. Chung and Lee considered the problem of finding a maximum matching in a convex bipartite graph, which has two sets of vertices, A and B, such that for any vertex v of A, the neighbors of v in B are contiguous. They gave a Boolean circuit for the problem in O(log ^2 n+log n· log log n· log b) depth and O(bn ^3 ) size, where n is the number of vertices in set A of the convex bipartite graph and b is the number of bits representing a vertex. Using Boolean circuits of prefix computation, odd-even merge, and some other parallel techniques, we present an improved Boolean circuit for the same problem in O(log ^2 n · (log b + log log n)) depth and O(bn ^2 log n) size.