Distributed Maintenance of Anytime Available Spanning Trees in Dynamic Networks

Abstract

We address the problem of building and maintaining a forest of spanning trees in highly dynamic networks, in which topological events can occur at any time and any rate, and no stable periods can be assumed. In these harsh environments, we strive to preserve some properties such as cycle-freeness or existence of a unique root in each fragment regardless of the events, so as to keep these fragments functioning uninterruptedly to a possible extent. Our algorithm operates at a coarse-grain level, using atomic pairwise interactions akin to population protocol or graph relabeling systems. The algorithm relies on a perpetual alternation of topology-induced splittings and computation-induced mergings of a forest of trees. Each tree in the forest hosts exactly one token (also called root) that performs a random walk inside the tree, switching parent-child relationships as it crosses edges. When two tokens are located on both sides of a same edge, their trees are merged upon this edge and one token disappears. Whenever an edge that belongs to a tree disappears, its child endpoint regenerates a new token instantly. The main features of this approach is that both merging and splitting are purely localized phenomenons. This paper presents the algorithm and establishes its correctness in arbitrary dynamic networks. We also discuss aspects related to the implementation of this general principle in fine-grain models, as well as embryonic elements of analysis. The characterization of the algorithm performance is left open, both analytically and experimentally.