Distributed Graph Diameter Approximation

• Main Authors: Matteo Ceccarello, Andrea Pietracaprina, Geppino Pucci, Eli Upfal
• Format: Article
• Language: English
• Published: MDPI AG 2020-09-01
• Series: Algorithms
• Subjects: graph analytics; parallel graph algorithms; weighted graph decomposition; weighted diameter approximation; MapReduce
• Online Access: https://www.mdpi.com/1999-4893/13/9/216

We present an algorithm for approximating the diameter of massive weighted undirected graphs on distributed platforms supporting a MapReduce-like abstraction. In order to be efficient in terms of both time and space, our algorithm is based on a decomposition strategy which partitions the graph into disjoint clusters of bounded radius. Theoretically, our algorithm uses linear space and yields a polylogarithmic approximation guarantee; most importantly, for a large family of graphs, it features a round complexity asymptotically smaller than the one exhibited by a natural approximation algorithm based on the state-of-the-art <inline-formula><math display="inline"><semantics><mi>Δ</mi></semantics></math></inline-formula>-stepping SSSP algorithm, which is its only practical, linear-space competitor in the distributed setting. We complement our theoretical findings with a proof-of-concept experimental analysis on large benchmark graphs, which suggests that our algorithm may attain substantial improvements in terms of running time compared to the aforementioned competitor, while featuring, in practice, a similar approximation ratio.