## Abstract

The minimum-weight 2-edge-connected spanning subgraph (2- ECSS) problem is a natural generalization of thewell-studied minimumweight spanning tree (MST) problem, and it has received considerable attention in the area of network design. The latter problem asks for a minimum-weight subgraph with an edge connectivity of 1 between each pair of vertices while the former strengthens this edge-connectivity requirement to 2. Despite this resemblance, the 2-ECSS problem is considerably more complex than MST. While MST admits a linear-time centralized exact algorithm, 2-ECSS is NP-hard and the best known centralized approximation algorithm for it (that runs in polynomial time) gives a 2-approximation. In this paper, we give a deterministic distributed algorithm with round complexity of HO(D+√n) that computes a (9+ϵ)-approximation of 2-ECSS, for any constant ϵ > 0. Up to logarithmic factors, this complexity matches the Ω(D + √n) lower bound that can be derived from the technique of Das Sarma et al. [STOC f11], as shown by Censor-Hillel and Dory [OPODIS f17]. Our result is the first distributed constant approximation for 2-ECSS in the nearly optimal time and it improves on a recent randomized algorithm of Dory [PODC f18], which achieved an O(logn)-approximation in HO(D +√n) rounds. We also present an alternative algorithm forO(logn)-approximation, whose round complexity is linear in the low-congestion shortcut parameter of the network.following a framework introduced by Ghaffari and Haeupler [SODA f16]. This algorithm has round complexity HO(D +√ n) in worst-case networks but it provably runs much faster in many well-behaved graph families of interest. For instance, it runs in HO(D) time in planar networks and those with bounded genus, bounded path-width or bounded tree-width.

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 | 521-530 |

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 Association for Computing Machinery. All rights reserved.

## Keywords

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

## ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications