A sharper analysis of a parallel algorithm for the all pairs shortest path problem

We consider the all pairs shortest path problem in a directed complete graph with n vertices, whose edge distances are non-negative random variables on parallel computers. We prove that the all pairs shortest path problem can be solved by the repeated “plus-min” algorithm for computing the closure of the distance matrix of the graph in O((n3/p)log log n) average time by p, 1 ≤ p ≤n3, processors on an SIMD-SM-RW computer for the graph whose edge distances are independent random variables drawn from [0, +∞] according to an arbitrary identical probability distribution.