### Abstract

We present an O(log d + log log_{m/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 language | English (US) |
---|---|

Title of host publication | SPAA 2020 - Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures |

Publisher | Association for Computing Machinery |

Pages | 359-369 |

Number of pages | 11 |

ISBN (Electronic) | 9781450369350 |

DOIs | |

State | Published - Jul 6 2020 |

Event | 32nd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2020 - Virtual, Online, United States Duration: Jul 15 2020 → Jul 17 2020 |

### Publication series

Name | Annual ACM Symposium on Parallelism in Algorithms and Architectures |
---|

### Conference

Conference | 32nd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2020 |
---|---|

Country | United States |

City | Virtual, Online |

Period | 7/15/20 → 7/17/20 |

### All Science Journal Classification (ASJC) codes

- Software
- Theoretical Computer Science
- Hardware and Architecture

### Keywords

- PRAM
- connected components
- hashing

## Fingerprint Dive into the research topics of 'Connected Components on a PRAM in Log Diameter Time'. Together they form a unique fingerprint.

## Cite this

*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