Near-Optimal Distributed Algorithms for Fault-Tolerant Tree Structures

Tree structures such as breadth-first search (BFS) trees and minimum spanning trees (MST) are among the most fundamental graph structures in distributed network algorithms. However, by definition, these structures are not robust against failures and even a single edge's removal can disrupt their functionality. A well-studied concept which attempts to circumvent this issue is Fault-Tolerant Tree Structures, where the tree gets augmented with additional edges from the network so that the functionality of the structure is maintained even when an edge fails. These structures, or other equivalent formulations, have been studied extensively from a centralized viewpoint. However, despite the fact that the main motivations come from distributed networks, their distributed construction has not been addressed before. In this paper, we present distributed algorithms for constructing fault tolerant BFS and MST structures. The time complexity of our algorithms are nearly optimal in the following strong sense: they almost match even the lower bounds of constructing (basic) BFS and MST trees.