## Abstract

We present fast algorithms for approximate shortest paths in the massively parallel computation (MPC) model. We provide randomized algorithms that take poly(łogłogn ) rounds in the near-linear memory MPC model. Our results are for unweighted undirected graphs with n vertices and m edges. Our first contribution is a (1+ϵ)-approximation algorithm for Single-Source Shortest Paths (SSSP) that takes poly(łogłogn ) rounds in the near-linear MPC model, where the memory per machine is Õ(n) and the total memory is Õ (mnρ ), where ρ is a small constant. Our second contribution is a distance oracle that allows to approximate the distance between any pair of vertices. The distance oracle is constructed in poly(łogłogn ) rounds and allows to query a (1+ϵ)(2k-1)-approximate distance between any pair of vertices u and v in O(1) additional rounds. The algorithm is for the near-linear memory MPC model with total memory of size Õ((m+n1+ρ )n1/k ), where ρ is a small constant. While our algorithms are for the near-linear MPC model, in fact they only use one machine with Õ(n) memory, where the rest of machines can have sublinear memory of size O(nγ) for a small constant γ< 1. All previous algorithms for approximate shortest paths in the near-linear MPC model either required ω(łogn ) rounds or had an ω(łogn ) approximation. Our approach is based on fast construction of near-additive emulators, limited-scale hopsets and limited-scale distance sketches that are tailored for the MPC model. While our end-results are for the near-linear MPC model, many of the tools we construct such as hopsets and emulators are constructed in the more restricted sublinear MPC model.

Original language | English |
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Title of host publication | SPAA 2024 - Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures |

Publisher | Association for Computing Machinery |

Pages | 415-426 |

Number of pages | 12 |

ISBN (Electronic) | 9798400704161 |

DOIs | |

State | Published - 17 Jun 2024 |

Event | 36th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2024 - Nantes, France Duration: 17 Jun 2024 → 21 Jun 2024 |

### Publication series

Name | Annual ACM Symposium on Parallelism in Algorithms and Architectures |
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ISSN (Print) | 1548-6109 |

### Conference

Conference | 36th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2024 |
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Country/Territory | France |

City | Nantes |

Period | 17/06/24 → 21/06/24 |

### Bibliographical note

Publisher Copyright:© 2024 Copyright held by the owner/author(s). Publication rights licensed to ACM.

## Keywords

- approximate shortest paths
- distance oracles
- emulators
- hopsets
- massively parallel computation

## ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Hardware and Architecture