Connected Components on a PRAM in Log Diameter Time

Sixue Cliff Liu, Robert E. Tarjan, Peilin Zhong

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationSPAA 2020 - Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures
PublisherAssociation for Computing Machinery
Pages359-369
Number of pages11
ISBN (Electronic)9781450369350
DOIs
StatePublished - Jul 6 2020
Event32nd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2020 - Virtual, Online, United States
Duration: Jul 15 2020Jul 17 2020

Publication series

NameAnnual ACM Symposium on Parallelism in Algorithms and Architectures

Conference

Conference32nd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2020
CountryUnited States
CityVirtual, Online
Period7/15/207/17/20

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture

Keywords

  • PRAM
  • connected components
  • hashing

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  • Cite this

    Liu, S. C., Tarjan, R. E., & Zhong, P. (2020). Connected Components on a PRAM in Log Diameter Time. In SPAA 2020 - Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures (pp. 359-369). (Annual ACM Symposium on Parallelism in Algorithms and Architectures). Association for Computing Machinery. https://doi.org/10.1145/3350755.3400249