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Connected Components on a PRAM in Log Diameter Time

Author(s): Liu, Sixue; Tarjan, Robert E; Zhong, Peilin

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Abstract: We present an O(log d + log logm/n n)-time randomized PRAM algorithm for computing the connected components of an n-vertex, m-edge undirected graph with maximum component diameter d. The algorithm runs on an ARBITRARY CRCW (concurrent-read, concurrent-write with arbitrary write resolution) PRAM using O(m) processors. The time bound holds with good probability. Our algorithm is based on the breakthrough results of Andoni et al. [FOCS'18] and Behnezhad et al. [FOCS'19]. Their algorithms run on the more powerful MPC model and rely on sorting and computing prefix sums in O(1) time, tasks that take Ω(log n / log log n) time on a CRCW PRAM with poly(n) processors. Our simpler algorithm uses limited-collision hashing and does not sort or do prefix sums. It matches the time and space bounds of the algorithm of Behnezhad et al., who improved the time bound of Andoni et al. It is widely believed that the larger private memory per processor and unbounded local computation of the MPC model admit algorithms faster than that on a PRAM. Our result suggests that such additional power might not be necessary, at least for fundamental graph problems like connected components and spanning forest.
Publication Date: Jul-2020
Citation: Liu, Sixue Cliff, Robert E. Tarjan, and Peilin Zhong. "Connected Components on a PRAM in Log Diameter Time." In Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures (2020): pp. 359-369. doi:10.1145/3350755.3400249
DOI: 10.1145/3350755.3400249
Pages: 359 - 369
Type of Material: Conference Article
Journal/Proceeding Title: Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures
Version: Author's manuscript

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