Vertex Reordering for Real-World Graphs and Applications: An Empirical Evaluation

Vertex reordering is a way to improve locality in graph computations. Given an input (or “natural”) order, reordering aims to compute an alternate permutation of the vertices that is aimed at maximizing a locality-based objective. Given decades of research on this topic, there are tens of graph reordering schemes, and there are also several linear arrangement “gap” measures for treatment as objectives. However, a comprehensive empirical analysis of the efficacy of the ordering schemes against the different gap measures, and against real-world applications is currently lacking. In this study, we present an extensive empirical evaluation of up to 11 ordering schemes, taken from different classes of approaches, on a set of 34 real-world graphs emerging from different application domains. Our study is presented in two parts: a) a thorough comparative evaluation of the different ordering schemes on their effectiveness to optimize different linear arrangement gap measures, relevant to preserving locality; and b) extensive evaluation of the impact of the ordering schemes on two real-world, parallel graph applications, namely, community detection and influence maximization. Our studies show a significant divergence among the ordering schemes (up to 40x between the best and the poor) in their effectiveness to reduce the gap measures; and a wide ranging impact of the ordering schemes on various aspects including application runtime (up to 4x), memory and cache use, load balancing, and parallel work and efficiency. The comparative study also helps in revealing the nuances of a parallel environment (compared to serial) on the ordering schemes and their role in optimizing applications.