A Faster Distributed Single-Source Shortest Paths Algorithm

We devise new algorithms for the single-source shortest paths 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 single-source shortest paths approximately, the fastest known exact algorithms are still far away from matching the lower bound of $\tilde \Omega (\sqrt{n} + D)$ 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 $\tilde O(n^{2/3} D^{1/3} + n^{5/6})$ rounds. We significantly improve upon this upper bound with our two new randomized algorithms, the first performing $\tilde O (\sqrt{n D})$ rounds and the second performing $\tilde O (\sqrt{n} D^{1/4} + n^{3/5} + D)$ rounds.