A Practical Parallel Algorithm for Diameter Approximation of Massive Weighted Graphs

TL;DR

This paper introduces a practical parallel algorithm for approximating the diameter of large weighted graphs efficiently on distributed systems, combining theoretical guarantees with extensive experimental validation.

Contribution

It presents a novel space- and time-efficient parallel algorithm with a new graph decomposition strategy, outperforming existing methods in practical scenarios.

Findings

Achieves substantial performance improvements over state-of-the-art algorithms.

Maintains a small constant approximation ratio below 1.4.

Operates with linear space and fewer rounds on important graph classes.

Abstract

We present a space and time efficient practical parallel algorithm for approximating the diameter of massive weighted undirected graphs on distributed platforms supporting a MapReduce-like abstraction. The core of the algorithm is a weighted graph decomposition strategy generating disjoint clusters of bounded weighted radius. Theoretically, our algorithm uses linear space and yields a polylogarithmic approximation guarantee; moreover, for important practical classes of graphs, it runs in a number of rounds asymptotically smaller than those required by the natural approximation provided by the state-of-the-art $\Delta$-stepping SSSP algorithm, which is its only practical linear-space competitor in the aforementioned computational scenario. We complement our theoretical findings with an extensive experimental analysis on large benchmark graphs, which demonstrates that our algorithm attains substantial improvements on a number of key performance indicators with respect to the aforementioned competitor, while featuring a similar approximation ratio (a small constant less than 1.4, as opposed to the polylogarithmic theoretical bound).