[{"date_created":"2023-07-23T22:01:12Z","department":[{"_id":"DaAl"},{"_id":"GradSch"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (in subscription journal)","ddc":["000"],"file_date_updated":"2023-07-31T10:53:08Z","conference":{"end_date":"2023-06-19","start_date":"2023-06-17","name":"SPAA: Symposium on Parallelism in Algorithms and Architectures","location":"Orlando, FL, United States"},"month":"06","quality_controlled":"1","publication_identifier":{"isbn":["9781450395458"]},"language":[{"iso":"eng"}],"doi":"10.1145/3558481.3591082","publisher":"Association for Computing Machinery","year":"2023","type":"conference","author":[{"last_name":"Fedorov","id":"2e711909-896a-11ed-bdf8-eb0f5a2984c6","first_name":"Alexander","full_name":"Fedorov, Alexander"},{"last_name":"Hashemi","id":"ed9595ea-2f8f-11ee-ba95-d2b546540783","first_name":"Diba","full_name":"Hashemi, Diba"},{"full_name":"Nadiradze, Giorgi","first_name":"Giorgi","last_name":"Nadiradze","id":"3279A00C-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0003-3650-940X","last_name":"Alistarh","id":"4A899BFC-F248-11E8-B48F-1D18A9856A87","full_name":"Alistarh, Dan-Adrian","first_name":"Dan-Adrian"}],"oa":1,"_id":"13262","date_published":"2023-06-17T00:00:00Z","arxiv":1,"citation":{"ista":"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.","mla":"Fedorov, Alexander, et al. “Provably-Efficient and Internally-Deterministic Parallel Union-Find.” <i>Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures</i>, Association for Computing Machinery, 2023, pp. 261–71, doi:<a href=\"https://doi.org/10.1145/3558481.3591082\">10.1145/3558481.3591082</a>.","short":"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.","apa":"Fedorov, A., Hashemi, D., Nadiradze, G., &#38; Alistarh, D.-A. (2023). Provably-efficient and internally-deterministic parallel Union-Find. In <i>Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures</i> (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>","ama":"Fedorov A, Hashemi D, Nadiradze G, Alistarh D-A. Provably-efficient and internally-deterministic parallel Union-Find. In: <i>Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures</i>. Association for Computing Machinery; 2023:261-271. doi:<a href=\"https://doi.org/10.1145/3558481.3591082\">10.1145/3558481.3591082</a>","chicago":"Fedorov, Alexander, Diba Hashemi, Giorgi Nadiradze, and Dan-Adrian Alistarh. “Provably-Efficient and Internally-Deterministic Parallel Union-Find.” In <i>Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures</i>, 261–71. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3558481.3591082\">https://doi.org/10.1145/3558481.3591082</a>.","ieee":"A. Fedorov, D. Hashemi, G. Nadiradze, and D.-A. Alistarh, “Provably-efficient and internally-deterministic parallel Union-Find,” in <i>Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures</i>, Orlando, FL, United States, 2023, pp. 261–271."},"scopus_import":"1","has_accepted_license":"1","publication":"Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures","external_id":{"arxiv":["2304.09331"]},"title":"Provably-efficient and internally-deterministic parallel Union-Find","file":[{"relation":"main_file","content_type":"application/pdf","access_level":"open_access","creator":"dernst","date_updated":"2023-07-31T10:53:08Z","success":1,"file_id":"13334","date_created":"2023-07-31T10:53:08Z","checksum":"72e312aabf0c5248c99b5cd3a88e4c88","file_size":2087937,"file_name":"2023_SPAA_Fedorov.pdf"}],"date_updated":"2023-07-31T10:54:32Z","status":"public","oa_version":"Published Version","publication_status":"published","page":"261-271","day":"17","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"abstract":[{"lang":"eng","text":"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."}]}]