## Abstract

In the minimum k-edge-connected spanning subgraph (k-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to k − 1 edge failures. This is a central problem in network design, and a natural generalization of the minimum spanning tree (MST) problem. While the MST problem has been studied extensively by the distributed computing community, for k ≥ 2 less is known in the distributed setting. In this paper, we present fast randomized distributed approximation algorithms for k-ECSS in the Congest model. Our first contribution is an O(D + n)-round O(log n)-approximation for 2-ECSS, for a graph with n vertices and diameter D. The time complexity of our algorithm is almost tight and almost matches the time complexity of the MST problem. For larger constant values of k we give an O(n)-round O(log n)-approximation. Additionally, in the special case of unweighted 3-ECSS we show how to improve the time complexity to O(D log^{3} n) rounds. All our results significantly improve the time complexity of previous algorithms.

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 |

Pages | 149-158 |

Number of pages | 10 |

ISBN (Print) | 9781450357951 |

DOIs | |

State | Published - 23 Jul 2018 |

Externally published | Yes |

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

### Publication series

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

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

City | Egham |

Period | 23/07/18 → 27/07/18 |

### Bibliographical note

Publisher Copyright:© 2018 Association for Computing Machinery.

## Keywords

- Approximation algorithms
- Distributed network design
- K-edge-connectivity

## ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications