Fast Distributed Computation of Distances in Networks

This paper presents a distributed algorithm to simultaneously compute the di-ameter, radius and node eccentricity in all nodes of a synchronous network. Such topological information may be useful as input to configure other algorithms. Pre-vious 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 estima-tions, 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 eccen-tricity 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.