## Abstract

We design fast deterministic algorithms for distance computation in the CONGESTED CLIQUE model. Our key contributions include: A (2+)-approximation for all-pairs shortest paths problem in O(log^{2}n / ) rounds on unweighted undirected graphs. With a small additional additive factor, this also applies for weighted graphs. This is the first sub-polynomial constant-factor approximation for APSP in this model. A (1+)-approximation for multi-source shortest paths problem from O(n) sources in O(log^{2} n / ) rounds on weighted undirected graphs. This is the first sub-polynomial algorithm obtaining this approximation for a set of sources of polynomial size. Our main techniques are new distance tools that are obtained via improved algorithms for sparse matrix multiplication, which we leverage to construct efficient hopsets and shortest paths. Furthermore, our techniques extend to additional distance problems for which we improve upon the state-of-the-art, including diameter approximation, and an exact single-source shortest paths algorithm for weighted undirected graphs in (n_{1/6}) rounds.

Original language | English |
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Title of host publication | PODC 2019 - Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing |

Publisher | Association for Computing Machinery |

Pages | 74-83 |

Number of pages | 10 |

ISBN (Electronic) | 9781450362177 |

DOIs | |

State | Published - 16 Jul 2019 |

Externally published | Yes |

Event | 38th ACM Symposium on Principles of Distributed Computing, PODC 2019 - Toronto, Canada Duration: 29 Jul 2019 → 2 Aug 2019 |

### Publication series

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

Conference | 38th ACM Symposium on Principles of Distributed Computing, PODC 2019 |
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Country/Territory | Canada |

City | Toronto |

Period | 29/07/19 → 2/08/19 |

### Bibliographical note

Publisher Copyright:© 2019 ACM.

## Keywords

- All-pairs shortest paths
- Congested clique
- Diameter
- Distributed computing
- Hopsets
- Matrix multiplication
- Single-source shortest paths
- approximation algorithms

## ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications