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arXiv · 1506.03265

A Practical Parallel Algorithm for Diameter Approximation of Massive Weighted Graphs

Matteo Ceccarello·Andrea Pietracaprina·Geppino Pucci·Eli Upfal
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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).

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Matteo Ceccarello, Andrea Pietracaprina, Geppino Pucci, Eli Upfal. 2015-06-10. A Practical Parallel Algorithm for Diameter Approximation of Massive Weighted Graphs. https://arxiv.org/abs/1506.03265

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