A Deterministic Distributed Algorithm for Exact Weighted All-Pairs Shortest Paths in $tilde{O}(n^{3/2})$ 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(n3/2) rounds in the Congest model, where n is the number of nodes in the graph. This is the first o(n2) 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, which has been used earlier in sequential dynamic computation of APSP.