## Abstract

We present improved deterministic algorithms for approximating shortest paths in the Congested Cliqe model of distributed computing. We obtain poly(log log n)-round algorithms for the following problems in unweighted undirected n-vertex graphs: • (1 + ∈)-approximation of multi-source shortest paths (MSSP) from [EQUATION] sources. • (2 + ∈)-approximation of all pairs shortest paths (APSP). • (1+∈, β)-approximation of APSP where [EQUATION]. These bounds improve exponentially over the state-of-the-art polylogarithmic bounds due to [Censor-Hillel et al., PODC19]. It also provides the first nearly-additive bounds for the APSP problem in sub-polynomial time. Our approach is based on distinguishing between short and long distances based on some distance threshold [EQUATION] where [EQUATION]. Handling the long distances is done by devising a new algorithm for computing a sparse (1 + ∈, β) emulator with O(n log log n) edges. For the short distances, we provide distance-sensitive variants for the distance tool-kit of [Censor-Hillel et al., PODC19]. By exploiting the fact that this tool-kit should be applied only on local balls of radius t, their round complexities get improved from poly (log n) to poly(log n). Finally, our deterministic solutions for these problems are based on a derandomization scheme of a novel variant of the hitting set problem, which might be of independent interest.

Original language | English |
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Title of host publication | PODC 2020 - Proceedings of the 39th Symposium on Principles of Distributed Computing |

Publisher | Association for Computing Machinery |

Pages | 59-68 |

Number of pages | 10 |

ISBN (Electronic) | 9781450375825 |

DOIs | |

State | Published - 31 Jul 2020 |

Externally published | Yes |

Event | 39th Symposium on Principles of Distributed Computing, PODC 2020 - Virtual, Online, Italy Duration: 3 Aug 2020 → 7 Aug 2020 |

### Publication series

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

Conference | 39th Symposium on Principles of Distributed Computing, PODC 2020 |
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Country/Territory | Italy |

City | Virtual, Online |

Period | 3/08/20 → 7/08/20 |

### Bibliographical note

Funding Information:Acknowledgments. We would like to thank Keren Censor-Hillel for many fruitful discussions. The research is supported in part by the Israel Science Foundation (grant no. 1696/14 and 2084/18), the European Union’s Horizon 2020 Research and Innovation Program under grant agreement no. 755839, and the Minerva grant no. 713238.

Publisher Copyright:

© 2020 ACM.

## Keywords

- congested clique
- near-additive emulator
- shortest paths

## ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications