In this paper we give three sub-cubic cost algorithms for the all pairs shortest distance (APSD) and path (APSP) problems. The rst is a parallel algorithm that solves the APSD problem for a directed graph with unit edge costs in O(log 2 n) time with O(n p logn) processors where = 2:688 on an EREW-PRAM. The second parallel algorithm solves the APSP, and consequently APSD, problem for a directed graph with non-negative general costs (real numbers) in O(log 2 n) time with o(n 3 ) subcubic costâ€¦Â CONTINUE READING