Brief announcement: Distributed approximation for tree augmentation

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.