## Abstract

We present O(log log n)-round algorithms in the Massively Parallel Computation (MPC) model, with Õ(n) memory per machine, that compute a maximal independent set, a 1 + approximation of maximum matching, and a 2 + approximation of minimum vertex cover, for any n-vertex graph and any constant > 0. These improve the state of the art as follows: • Our MIS algorithm leads to a simple O(log log ∆)-round MIS algorithm in the CONGESTED-CLIQUE model of distributed computing, which improves on the Õ(log ∆)-round algorithm of Ghaffari [PODC'17]. • Our O(log log n)-round (1+)-approximate maximum matching algorithm simplifies or improves on the following prior work: O(log^{2} log n)-round (1 +)-approximation algorithm of Czumaj et al. [STOC'18] and O(log log n)-round (1 + )- approximation algorithm of Assadi et al. [arXiv'17]. • Our O(log log n)-round (2 +)-approximate minimum vertex cover algorithm improves on an O(log log n)-round O(1)approximation of Assadi et al. [arXiv'17].

Original language | English |
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Title of host publication | PODC 2018 - Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing |

Publisher | Association for Computing Machinery (ACM) |

Pages | 129-138 |

Number of pages | 10 |

ISBN (Print) | 9781450357951 |

DOIs | |

Publication status | Published - 23 Jul 2018 |

Event | 37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018 - Egham, United Kingdom Duration: 23 Jul 2018 → 27 Jul 2018 |

### Conference

Conference | 37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018 |
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Country | United Kingdom |

City | Egham |

Period | 23/07/18 → 27/07/18 |

## Keywords

- Congested clique
- Massively parallel computation
- Maximal independent set
- Maximum matching
- Vertex cover