A Faster Distributed Single-Source Shortest Paths Algorithm

We devise new algorithms for the single-source shortest paths (SSSP) problem in the CONGEST model of distributed computing. While close-to-optimal solutions, in terms of the number of rounds spent by the algorithm, have recently been developed for computing SSSP approximately, the fastest known exact algorithms are still far away from matching the lower bound of Ω̃( √ n +D) rounds by Peleg and Rubinovich [SICOMP’00], where n is the number of nodes in the network and D is its diameter. The state of the art is Elkin’s randomized algorithm [STOC’17] that performs Õ(n2/3D1/3 +n5/6) rounds. We signi cantly improve upon this upper bound with our two new randomized algorithms, the rst performing Õ( √ nD) rounds and the second performing Õ( √ nD1/4 +n3/5 +D) rounds. Our bounds also compare favorably to the independent result by Gha ari and Li [STOC’18]. As side results, we obtain a (1 + ε)approximation Õ(( √ nD1/4 + D)/ε)-round algorithm for directed SSSP and a new work/depth trade-o for exact SSSP on directed graphs in the PRAM model.