Unison as a Self-Stabilizing Wave Stream Algorithm in Asynchronous Anonymous Networks

TL;DR

This paper introduces a novel self-stabilizing wave stream algorithm called Unison for anonymous networks, enabling global information propagation and synchronization without leader election, using probabilistic and wave-based methods.

Contribution

It presents the first self-stabilizing wave stream algorithm in anonymous networks, utilizing Unison for barrier synchronization and introducing strong waves and wavelets for various computations.

Findings

Design of a self-stabilizing barrier synchronization in anonymous networks.

Development of self-stabilizing wave streams, including strong waves and wavelets.

Application of these waves to solve idempotent operator and k-distance computations.

Abstract

How to pass from local to global scales in anonymous networks? How to organize a selfstabilizing propagation of information with feedback. From the Angluin impossibility results, we cannot elect a leader in a general anonymous network. Thus, it is impossible to build a rooted spanning tree. Many problems can only be solved by probabilistic methods. In this paper we show how to use Unison to design a self-stabilizing barrier synchronization in an anonymous network. We show that the commuication structure of this barrier synchronization designs a self-stabilizing wave-stream, or pipelining wave, in anonymous networks. We introduce two variants of Wave: the strong waves and the wavelets. A strong wave can be used to solve the idempotent r-operator parametrized computation problem. A wavelet deals with k-distance computation. We show how to use Unison to design a self-stabilizing wave stream, a self-stabilizing strong wave stream and a self-stabilizing wavelet stream.