Distributed Maintenance of Anytime Available Spanning Trees in Dynamic Networks

TL;DR

This paper presents a distributed algorithm for maintaining spanning trees in highly dynamic networks, ensuring properties like cycle-freeness and root existence through localized merging and splitting operations.

Contribution

It introduces a novel, localized approach using token-based random walks for continuous maintenance of spanning trees in unpredictable network topologies.

Findings

Algorithm maintains spanning trees with high reliability in dynamic environments.

Expected merging time for trees is analytically characterized.

The approach is proven correct in arbitrary dynamic networks.

Abstract

We address the problem of building and maintaining distributed 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 the existence of a root in each tree, in order to make it possible to keep using the trees uninterruptedly (to a possible extent). Our algorithm operates at a coarse-grain level, using atomic pairwise interactions in a way akin to recent population protocol models. The algorithm relies on a perpetual alternation of \emph{topology-induced splittings} and \emph{computation-induced mergings} of a forest of spanning trees. Each tree in the forest hosts exactly one token (also called root) that performs a random walk {\em 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 \emph{merging} and \emph{splitting} are purely localized phenomenons. In this paper, we present and motivate the algorithm, and we prove its correctness in arbitrary dynamic networks. Then we discuss several implementation choices around this general principle. Preliminary results regarding its analysis are also discussed, in particular an analytical expression of the expected merging time for two given trees in a static context.