Maintaining a Distributed Spanning Forest in Highly Dynamic Networks

Abstract

Highly dynamic networks are characterized by frequent changes in the availability of communication links. These networks are often partitioned into several components, which split and merge unpredictably. We present a distributed algorithm that maintains a forest of (as few as possible) spanning trees in such a network, with no restriction on the rate of change. Our algorithm is inspired by highlevel graph transformations, which we adapt here in a (synchronous) message passing model for dynamic networks. The resulting algorithm has the following properties: First, every decision is purely local-in each round, a node only considers its role and that of its neighbors in the tree, with no further information propagation (in particular, no wave mechanisms). Second, whatever the rate and scale of the changes, the algorithm guarantees that, by the end of every round, the network is covered by a forest of spanning trees in which 1) no cycle occur, 2) every node belongs to exactly one tree, and 3) every tree contains exactly one root (or token). We primarily focus on the correctness of this algorithm, which is established rigorously. While performance is not the main focus, we suggest new complexity metrics for such problems, and report on preliminary experimentation results validating our algorithm in a practical scenario. * A preliminary version of this work (without proofs of correctness and much revisited since) was presented at the 18th Int. Conf. on Principles of Distributed Systems (OPODIS, 2014).

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“…In fact, the problem of testing whether a dynamic graph is temporally connected has been studied before in various settings [7,9,33]. The authors of [9] propose an algorithm for computing foremost journeys in a model of evolving graphs, where nodes and edges are associated with lists of time intervals, representing their existence over time, and each edge has a traversal time.…”

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