## Abstract

A minimum spanning tree (MST) is an essential structure for distributed algorithms, since it is a low-cost connected subgraph which provides an efficient way to communicate in a network. However, trees cannot survive even one link failure. In this paper, we study the Tree Augmentation Problem (TAP), for which the input is a graph G and a spanning tree T of G and the goal is to augment T with a minimum (or minimum weight) set of edges Aug from G, such that T ∪ Aug remains connected after a failure of any single link. Being central tasks for network design, TAP and additional connectivity augmentation problems have been well studied in the sequential setting. However, despite the distributed nature of these problems, they have not been studied in the distributed setting. We address this fundamental topic and provide a study of distributed TAP. In the full version of this paper, we present distributed 2-approximation algorithms for TAP, both for the unweighted and weighted versions, which have a time complexity of O(h) rounds, where h is the height of T. We also present a distributed 4-approximation for unweighted TAP that has a time complexity of O(√n log∗ n+D) rounds for a graph G with n vertices and diameter D, which is an improvement for large values of h. We complement our algorithms with lower bounds and some applications to related problems.

Original language | English |
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Title of host publication | PODC 2017 - Proceedings of the ACM Symposium on Principles of Distributed Computing |

Publisher | Association for Computing Machinery |

Pages | 199-201 |

Number of pages | 3 |

ISBN (Electronic) | 9781450349925 |

DOIs | |

State | Published - 26 Jul 2017 |

Externally published | Yes |

Event | 36th ACM Symposium on Principles of Distributed Computing, PODC 2017 - Washington, United States Duration: 25 Jul 2017 → 27 Jul 2017 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Principles of Distributed Computing |
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Volume | Part F129314 |

### Conference

Conference | 36th ACM Symposium on Principles of Distributed Computing, PODC 2017 |
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Country/Territory | United States |

City | Washington |

Period | 25/07/17 → 27/07/17 |

### Bibliographical note

Funding Information:∗Supported in part by the Israel Science Foundation (grant 1696/14).

Publisher Copyright:

© 2017 Association for Computing Machinery.

## Keywords

- Approximation algorithms
- Connectivity augmentation
- Distributed network design

## ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications