A Deterministic Distributed Algorithm for Exact Weighted All-Pairs Shortest Paths in Õ(n 3/2 ) Rounds

We present a deterministic distributed algorithm to compute all-pairs shortest paths (APSP) in an edge-weighted directed or undirected graph. Our algorithm runs in O (n^3/2 ) rounds in the Congest model, where n is the number of nodes in the graph. This is the first o(n^2) rounds deterministic distributed algorithm for the weighted APSP problem. Our algorithm is fairly simple and incorporates a deterministic distributed algorithm we develop for computing a 'blocker set' [King99], which has been used earlier in sequential dynamic computation of APSP.