A Practical Parallel Algorithm for Diameter Approximation of Massive Weighted Graphs

We present a space/time-efficient practical parallel algorithm for approximating the diameter of massive 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. The number of parallel rounds executed by the algorithm is proportional to the unweighted radius of the clusters, and can be significantly smaller than the number of rounds required by the natural SSSP-based approximation algorithm, which is the only practical competitor in the aformentioned computational scenario. We present an extensive experimental analysis testing various design choices, which result into an implementation featuring a good approximation ratio (less than 1.5 versus the theoretical $O(\log^3 n)$ bound) and running times which are up to one order of magnitude faster than the SSSP-based competitor, on a number of very large benchmark graphs.