A provably fastest parallel algorithm for the recognition of the consecutive ones property with selected applications

Presented here is a parallel algorithm that decides if an m/spl times/n (0, 1)-matrix has the consecutive 1's property for rows, and if so, turns the matrix into one with consecutive 1's in each row by column permutation. The algorithm runs in optimal O(log(mn)) time with O(M(m)n log m/m+M(n)m/sup 2/ log n/n/sup 2/) work on CREW PRAM where M(n) denotes the processor bound for multiplying two n/spl times/n matrices in O(log n) time and is o(n/sup 2.376/). We then show that this procedure can recognize doubly convex bipartite graphs in O(log n) time with O(M(n)) processors.