Distributed Exact Weighted All-Pairs Shortest Paths in $\tilde O(n^{5/4})$ Rounds

We study computing {\em all-pairs shortest paths} (APSP) on distributed networks (the CONGEST model). The goal is for every node in the (weighted) network to know the distance from every other node using communication. The problem admits $(1+o(1))$-approximation $\tilde O(n)$-time algorithms ~\cite{LenzenP-podc15,Nanongkai-STOC14}, whic...More