Distributed Self-Stabilizing MIS with Few States and Weak Communication

Abstract

We consider self-stabilizing algorithms to compute a Maximal Independent Set (MIS) in the extremely weak beeping communication model. The model consists of an anonymous network with synchronous rounds. In each round, each vertex can optionally transmit a signal to all its neighbors (beep). After the transmission of a signal, each vertex can only differentiate between no signal received, or at least one signal received. We assume that vertices have some knowledge about the topology of the network.We revisit the not self-stabilizing algorithm proposed by Jeavons, Scott, and Xu ( 2013), which computes an MIS in the beeping model. We enhance this algorithm to be selfstabilizing, and explore two different variants, which differ in the knowledge about the topology available to the vertices. In the first variant, every vertex knows an upper bound on the maximum degree ∆ of the graph. For this case, we prove that the proposed self-stabilizing version maintains the same run-time as the original algorithm, i.e. it stabilizes after O(log n) rounds w.h.p. on any n-vertex graph. In the second variant, each vertex only knows an upper bound on its own degree. For this case, we prove that the algorithm stabilizes after O(log n • log log n) rounds on any n-vertex graph, w.h.p.

Non-negotiating Distributed Computing

“…Many of these works considered synchronous failure-free distributed computing. Others considered asynchronous models, including work assuming noisy communication channels [13], work on self-stabilizing systems in which processes are subject to transient failures [20], and a few other contributions to asynchronous shared-memory computing to understand, e.g., epigenetic cell modification [33].…”