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

How to pass from local to global scales in anonymous networks? In such networks, how to organize a self-stabilizing propagation of information with feedback? From Angluin’s results, the deterministic leader election is impossible in general anonymous networks. Thus, it is impossible to build a rooted spanning tree. In this paper we show how to use Unison to design a selfstabilizing barrier synchronization in an anonymous network. We show that the communication structure of this barrier synchronization designs a self-stabilizing wave stream, or pipelined wave, in anonymous networks. We introduce two variants of waves: Strong Wave and Wavelet. Strong waves can be used to solve the idempotent r-operator parametrized problem, which implies well known problems like depth-first search tree construction – this instance requires identities for the processors. Wavelets deal with ρ-distance computation. We show how to use Unison to design a self-stabilizing strong wave stream, and wavelet stream respectively.