Provably-efficient and internally-deterministic parallel Union-Find

conference paper Provably-efficient and internally-deterministic parallel Union-Find published yes Alexander Fedorov author 2e711909-896a-11ed-bdf8-eb0f5a2984c6 Diba Hashemi author ed9595ea-2f8f-11ee-ba95-d2b546540783 Giorgi Nadiradze author 3279A00C-F248-11E8-B48F-1D18A9856A870000-0001-5634-0731 Dan-Adrian Alistarh author 4A899BFC-F248-11E8-B48F-1D18A9856A870000-0003-3650-940X DaAl department GradSch department SPAA: Symposium on Parallelism in Algorithms and Architectures Determining the degree of inherent parallelism in classical sequential algorithms and leveraging it for fast parallel execution is a key topic in parallel computing, and detailed analyses are known for a wide range of classical algorithms. In this paper, we perform the first such analysis for the fundamental Union-Find problem, in which we are given a graph as a sequence of edges, and must maintain its connectivity structure under edge additions. We prove that classic sequential algorithms for this problem are well-parallelizable under reasonable assumptions, addressing a conjecture by [Blelloch, 2017]. More precisely, we show via a new potential argument that, under uniform random edge ordering, parallel union-find operations are unlikely to interfere: T concurrent threads processing the graph in parallel will encounter memory contention O(T2 · log |V| · log |E|) times in expectation, where |E| and |V| are the number of edges and nodes in the graph, respectively. We leverage this result to design a new parallel Union-Find algorithm that is both internally deterministic, i.e., its results are guaranteed to match those of a sequential execution, but also work-efficient and scalable, as long as the number of threads T is O(|E|1 over 3 - ε), for an arbitrarily small constant ε > 0, which holds for most large real-world graphs. We present lower bounds which show that our analysis is close to optimal, and experimental results suggesting that the performance cost of internal determinism is limited. https://research-explorer.ista.ac.at/download/13262/13334/2023_SPAA_Fedorov.pdf application/pdfno Association for Computing Machinery2023Orlando, FL, United States eng Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures 9781450395458 2304.09331 00110888900002410.1145/3558481.3591082 261-271 Fedorov, Alexander, et al. “Provably-Efficient and Internally-Deterministic Parallel Union-Find.” Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures, Association for Computing Machinery, 2023, pp. 261–71, doi:<a href="https://doi.org/10.1145/3558481.3591082">10.1145/3558481.3591082</a>. Fedorov, A., Hashemi, D., Nadiradze, G., & Alistarh, D.-A. (2023). Provably-efficient and internally-deterministic parallel Union-Find. In Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures (pp. 261–271). Orlando, FL, United States: Association for Computing Machinery. <a href="https://doi.org/10.1145/3558481.3591082">https://doi.org/10.1145/3558481.3591082</a> Fedorov A, Hashemi D, Nadiradze G, Alistarh D-A. 2023. Provably-efficient and internally-deterministic parallel Union-Find. Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures. SPAA: Symposium on Parallelism in Algorithms and Architectures, 261–271. A. Fedorov, D. Hashemi, G. Nadiradze, D.-A. Alistarh, in:, Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures, Association for Computing Machinery, 2023, pp. 261–271. Fedorov, Alexander, Diba Hashemi, Giorgi Nadiradze, and Dan-Adrian Alistarh. “Provably-Efficient and Internally-Deterministic Parallel Union-Find.” In Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures, 261–71. Association for Computing Machinery, 2023. <a href="https://doi.org/10.1145/3558481.3591082">https://doi.org/10.1145/3558481.3591082</a>. A. Fedorov, D. Hashemi, G. Nadiradze, and D.-A. Alistarh, “Provably-efficient and internally-deterministic parallel Union-Find,” in Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures, Orlando, FL, United States, 2023, pp. 261–271. Fedorov A, Hashemi D, Nadiradze G, Alistarh D-A. Provably-efficient and internally-deterministic parallel Union-Find. In: Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures. Association for Computing Machinery; 2023:261-271. doi:<a href="https://doi.org/10.1145/3558481.3591082">10.1145/3558481.3591082</a> 132622023-07-23T22:01:12Z2025-09-09T12:43:18Z