Single-Source Shortest Paths in the CONGEST Model with Improved Bound

Abstract

We improve the time complexity of the single-source shortest path problem for weighted directed graphs (with non-negative integer weights) in the Broadcast CONGEST model of distributed computing. For polynomially bounded edge weights, the state-of-the-art algorithm for this problem requires [EQUATION] rounds [Forster and Nanongkai, FOCS 2018], which is quite far from the known lower bound of [EQUATION] rounds [Elkin, STOC 2014]; here D is the diameter of the underlying network and n is the number of vertices in it. For the approximate version of this problem, Forster and Nanongkai [FOCS 2018] obtained an upper bound of [EQUATION], and stated that achieving the same bound for the exact case remains a major open problem. In this paper we resolve the above mentioned problem by devising a new randomized algorithm for solving (the exact version of) this problem in [EQUATION] rounds. Our algorithm is based on a novel weight-modifying technique that allows us to compute bounded-hop distance approximation that preserves a certain form of the triangle inequality for the edges in the graph.