Parallel Index-Based Structural Graph Clustering and Its Approximation

TL;DR

This paper introduces a parallel, index-based SCAN algorithm for graph clustering that significantly accelerates query times and index construction on large graphs, with provable efficiency and approximate clustering guarantees.

Contribution

It presents a practical parallel index construction method for SCAN using GS*-Index and LSH, improving speed and scalability over existing algorithms with theoretical guarantees.

Findings

Parallel index construction achieves 50-151x speedup over GS*-Index.

Parallel query processing is 5-32x faster than GS*-Index.

LSH-based approximation maintains clustering quality while speeding up index creation.

Abstract

SCAN (Structural Clustering Algorithm for Networks) is a well-studied, widely used graph clustering algorithm. For large graphs, however, sequential SCAN variants are prohibitively slow, and parallel SCAN variants do not effectively share work among queries with different SCAN parameter settings. Since users of SCAN often explore many parameter settings to find good clusterings, it is worthwhile to precompute an index that speeds up queries. This paper presents a practical and provably efficient parallel index-based SCAN algorithm based on GS*-Index, a recent sequential algorithm. Our parallel algorithm improves upon the asymptotic work of the sequential algorithm by using integer sorting. It is also highly parallel, achieving logarithmic span (parallel time) for both index construction and clustering queries. Furthermore, we apply locality-sensitive hashing (LSH) to design a novel approximate SCAN algorithm and prove guarantees for its clustering behavior. We present an experimental evaluation of our algorithms on large real-world graphs. On a 48-core machine with two-way hyper-threading, our parallel index construction achieves 50--151$\times$ speedup over the construction of GS*-Index. In fact, even on a single thread, our index construction algorithm is faster than GS*-Index. Our parallel index query implementation achieves 5--32$\times$ speedup over GS*-Index queries across a range of SCAN parameter values, and our implementation is always faster than ppSCAN, a state-of-the-art parallel SCAN algorithm. Moreover, our experiments show that applying LSH results in faster index construction while maintaining good clustering quality.