Fast Distributed Computation of Distances in Networks

TL;DR

This paper introduces a fast distributed algorithm for computing the diameter, radius, and node eccentricity in networks, improving convergence speed by avoiding BFS trees and using estimations propagation.

Contribution

The paper presents a novel distributed algorithm that accelerates the computation of network topological metrics without constructing BFS trees, using local criteria for convergence detection.

Findings

Achieves faster convergence to topological metrics

Operates without BFS tree construction

Provides local convergence detection criteria

Abstract

This paper presents a distributed algorithm to simultaneously compute the diameter, radius and node eccentricity in all nodes of a synchronous network. Such topological information may be useful as input to configure other algorithms. Previous approaches have been modular, progressing in sequential phases using building blocks such as BFS tree construction, thus incurring longer executions than strictly required. We present an algorithm that, by timely propagation of available estimations, achieves a faster convergence to the correct values. We show local criteria for detecting convergence in each node. The algorithm avoids the creation of BFS trees and simply manipulates sets of node ids and hop counts. For the worst scenario of variable start times, each node i with eccentricity ecc(i) can compute: the node eccentricity in diam(G)+ecc(i)+2 rounds; the diameter in 2*diam(G)+ecc(i)+2 rounds; and the radius in diam(G)+ecc(i)+2*radius(G) rounds.