## Abstract

In this work we present the first constant-round algorithms for computing spanners and approximate All-Pairs Shortest Paths (APSP) in the distributed CONGESTED CLIQUE model. Specifically, we show the following results for undirected n-node graphs. ulFor every integer k ≥ 1, O(1)-round algorithms for constructing O(k)-spanners with O(n1+1/k) edges in unweighted graphs, and O(k)-spanners with O(n1+1/k log n) edges in weighted graphs. An O(1)-round algorithm for O(log n)-approximation for APSP in unweighted graphs. An O(1)-round algorithm for O(log2n)-approximation for APSP in weighted graphs. All our algorithms are randomized and succeed with high probability. Prior to our work, the fastest algorithms for computing O(k)-spanners in this model require poly(log k) rounds [Parter, Yogev, DISC '18] [Biswas et al., SPAA '21], and the fastest algorithms for approximate shortest paths require poly(log log n) rounds [Dory, Parter, PODC '20]. Our results extend to the closely related massively parallel computation (MPC) model with near-linear memory per machine, leading to the first O(1)-round algorithms for spanners and approximate shortest paths in this model as well.

Original language | English |
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Title of host publication | PODC 2021 - Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing |

Publisher | Association for Computing Machinery |

Pages | 223-233 |

Number of pages | 11 |

ISBN (Electronic) | 9781450385480 |

DOIs | |

State | Published - 21 Jul 2021 |

Externally published | Yes |

Event | 40th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2021 - Virtual, Online, Italy Duration: 26 Jul 2021 → 30 Jul 2021 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Principles of Distributed Computing |
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### Conference

Conference | 40th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2021 |
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Country/Territory | Italy |

City | Virtual, Online |

Period | 26/07/21 → 30/07/21 |

### Bibliographical note

Publisher Copyright:© 2021 ACM.

## Keywords

- congested clique
- massively parallel computation
- shortest paths
- spanners

## ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications