  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).
