Parallel Algorithms for Hierarchical Nucleus Decomposition

TL;DR

This paper introduces scalable parallel algorithms for hierarchy construction in nucleus decomposition, enabling efficient dense subgraph analysis with theoretical guarantees and significant speedups over existing methods.

Contribution

It presents a novel parallel hierarchy construction algorithm and a parallel approximation method with proven bounds, improving efficiency and scalability in dense subgraph analysis.

Findings

Up to 58.84x speedup over sequential algorithms

Approximation algorithm achieves 3.3x speedup with 1.33x error

Strong theoretical bounds on work and span

Abstract

Nucleus decompositions have been shown to be a useful tool for finding dense subgraphs. The coreness value of a clique represents its density based on the number of other cliques it is adjacent to. One useful output of nucleus decomposition is to generate a hierarchy among dense subgraphs at different resolutions. However, existing parallel algorithms for nucleus decomposition do not generate this hierarchy, and only compute the coreness values. This paper presents a scalable parallel algorithm for hierarchy construction, with practical optimizations, such as interleaving the coreness computation with hierarchy construction and using a concurrent union-find data structure in an innovative way to generate the hierarchy. We also introduce a parallel approximation algorithm for nucleus decomposition, which achieves much lower span in theory and better performance in practice. We prove strong theoretical bounds on the work and span (parallel time) of our algorithms. On a 30-core machine with two-way hyper-threading on real-world graphs, our parallel hierarchy construction algorithm achieves up to a 58.84x speedup over the state-of-the-art sequential hierarchy construction algorithm by Sariyuce et al. and up to a 30.96x self-relative parallel speedup. On the same machine, our approximation algorithm achieves a 3.3x speedup over our exact algorithm, while generating coreness estimates with a multiplicative error of 1.33x on average.