Renovating Watts and Strogatz Random Graph Generation by a Sequential Approach

Abstract

Numerous data intensive applications call for generating gigantic random graphs. The Watts-Strogatz model is well noted as a fundamental, versatile yet simple random graph model. The Watts-Strogatz model simulates the “small world” phenomenon in real-world graphs that includes short average path lengths and high clustering. However, the existing algorithms for the Watts-Strogatz model are not scalable. This study proposes a sequential algorithm termed ZWS that generates exact Watts-Strogatz graphs with fewer iterations than the state-of-the-art Watts-Strogatz algorithm and therefore faster. Given the so-called edge rewiring probability p (0 ≤ p≤ 1 ) of the Watts-Strogatz model and m neighbouring nodes of v nodes, ZWS needs p× m× v random decisions while the state-of-the-art Watts-Strogatz algorithm needs m× v, such that for large graphs with small probability, ZWS is able to generate Watts-Strogatz graphs with substantially less iterations. However, the less iterations in ZWS requires complex computation which avoids ZWS to achieve its full practical speedup. Therefore, we further improve our solution as PreZWS that enhances ZWS algorithm through pre-computation techniques to substantially speedup the overall generation process practically. Extensive experiments show the efficiency and effectiveness of the proposed scheme, e.g., PreZWS yields average speedup of 2 times over the state-of-the-art algorithm on a single machine.