## 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 |
---|---|

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 |
---|

### Conference

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

Country/Territory | Italy |

City | Virtual, Online |

Period | 26/07/21 → 30/07/21 |

### Bibliographical note

Funding Information:We thank Sara Ratzon and Maayan Lusting for hosting us in their breathtaking Airbnb apartment in the Sea of Galilee, where we have conducted part of this research. We also thank the anonymous reviewers for their valuable feedback. This project is supported in part by the Swiss National Foundation (project grant 200021_184735). This project has also received funding from the European Union’s Horizon 2020 Research and Innovation Program under grant agreement no. 755839. The third-named author is supported by the Defense Advanced Research Projects Agency (DARPA) under agreement number HR00112020023. The third-named author also acknowledges the Simons institute for the generous hosting and support.

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