2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)

All-Pairs Shortest Paths (APSP) is one of the most basic problems in graph algorithms. Given an $n$-node directed or undirected graph with integer weights in $\{-n^{c}, \ldots, n^{c}\}$ and no negative cycles, APSP asks to compute the shortest paths distance between every pair of vertices. The fastest known algorithm for APSP runs in $n^{3}/2^{\Theta(\sqrt{\log n})}$ time [Williams'14], and no truly subcubic time algorithms are known. One of the main hypotheses in fine-grained complexity is… CONTINUE READING