A Deterministic Distributed Algorithm for Exact Weighted All-Pairs Shortest Paths in $\tilde{O}(n^{3/2})$ Rounds

TL;DR

This paper introduces a simple deterministic distributed algorithm for exact weighted all-pairs shortest paths that runs in sub-quadratic rounds, improving over previous methods and utilizing a blocker set computation.

Contribution

It presents the first deterministic distributed algorithm for weighted APSP with sub-quadratic round complexity, using a novel blocker set approach.

Findings

Runs in O(n^{3/2}) rounds in the Congest model

First deterministic distributed algorithm for weighted APSP with o(n^2) rounds

Uses a new deterministic blocker set computation method

Abstract

We present a deterministic distributed algorithm to compute all-pairs shortest paths(APSP) in an edge-weighted directed or undirected graph. Our algorithm runs in $\tilde{O}(n^{3/2})$ rounds in the Congest model, where $n$ is the number of nodes in the graph. This is the first $o(n^2)$ rounds deterministic distributed algorithm for the weighted APSP problem. Our algorithm is fairly simple and incorporates a deterministic distributed algorithm we develop for computing a `blocker set' \cite{King99}, which has been used earlier in sequential dynamic computation of APSP.