## Abstract

Over the past decade, there has been increasing interest in distributed/parallel algorithms for processing large-scale graphs. By now, we have quite fast algorithms - -usually sublogarithmic-time and often poly(łogłog n)-time, or even faster - -for a number of fundamental graph problems in the massively parallel computation (MPC) model. This model is a widely-adopted theoretical abstraction of MapReduce style settings, where a number of machines communicate in an all-to-all manner to process large-scale data. Contributing to this line of work on MPC graph algorithms, we present poly(łog k) ϵ poly(łogłog n) round MPC algorithms for computing O(k^1+o(1) )-spanners in the strongly sublinear regime of local memory. To the best of our knowledge, these are the first sublogarithmic-time MPC algorithms for spanner construction. As primary applications of our spanners, we get two important implications, as follows: -For the MPC setting, we get an O(łog^2łog n)-round algorithm for O(łog^1+o(1) n) approximation of all pairs shortest paths (APSP) in the near-linear regime of local memory. To the best of our knowledge, this is the first sublogarithmic-time MPC algorithm for distance approximations. -Our result above also extends to the Congested Clique model of distributed computing, with the same round complexity and approximation guarantee. This gives the first sub-logarithmic algorithm for approximating APSP in weighted graphs in the Congested Clique model.

Original language | English |
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Title of host publication | SPAA 2021 - Proceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures |

Publisher | Association for Computing Machinery |

Pages | 118-128 |

Number of pages | 11 |

ISBN (Electronic) | 9781450380706 |

DOIs | |

State | Published - 6 Jul 2021 |

Externally published | Yes |

Event | 33rd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2021 - Virtual, Online, United States Duration: 6 Jul 2021 → 8 Jul 2021 |

### Publication series

Name | Annual ACM Symposium on Parallelism in Algorithms and Architectures |
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### Conference

Conference | 33rd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2021 |
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Country/Territory | United States |

City | Virtual, Online |

Period | 6/07/21 → 8/07/21 |

### Bibliographical note

Publisher Copyright:© 2021 ACM.

## Keywords

- Massively parallel computation
- Shortest paths
- Spanners

## ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Hardware and Architecture