Parallel Algorithms for Hierarchical Nucleus Decomposition
Author(s)
Shi, Jessica
Dhulipala, Laxman
Shun, Julian
Date Issued
March 12, 2024
Journal
Proceedings of the ACM on Management of Data
Publisher
Association for Computing Machinery
Citation
Jessica Shi, Laxman Dhulipala, and Julian Shun. 2024. Parallel Algorithms for Hierarchical Nucleus Decomposition. Proc. ACM Manag. Data 2, 1 (SIGMOD), Article 32 (February 2024), 27 pages.
Version
Final published version
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, 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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
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Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/3639287
