Scalable algorithms for compact spanners on real world graphs

Abstract

A graph spanner is a subgraph that preserves the shortest distance between every pair of vertices within a permissible distortion. Typically, the allowed distortion is a multiplicative factor (of the original distances) and is referred to as stretch. Efficient multiplicative spanners, based on finding low diameter decompositions, have been studied in the distributed and parallel settings. Most of these studies aim to find spanners with theoretical guarantees on the stretch and spanner size. The spanner size guarantees obtained in these works are not very useful for real world sparse graphs. In this work, we evaluate and compare the state of the art algorithms for multiplicative spanners on real world and synthetic graphs. We propose a heuristic that aims to reduce the size of the output spanner. When combined with existing approaches, it admits similar theoretical guarantees as described in prior work while yielding considerably smaller spanners. Our heuristic builds on the idea of selecting centers with large neighborhoods and growing clusters around them. We present a parallel algorithm for selecting a large set of cluster centers based on this heuristic. We evaluate our algorithms on 18 real world graphs from the SNAP data set and 3 well studied synthetic graphs. We demonstrate that our heuristic yields spanners with significantly fewer edges - up to 6x smaller on real world graphs and up to 20x smaller on synthetic graphs, compared to baselines from prior work.