Acyclic Strategy for Silent Self-Stabilization in Spanning Forests

TL;DR

This paper introduces a general approach for designing silent self-stabilizing algorithms in networks with spanning forests, ensuring correctness and optimal stabilization time under unfair scheduling.

Contribution

It formalizes design patterns for self-stabilizing algorithms in spanning forests, proving their correctness, silence, and optimal stabilization time.

Findings

Algorithms are silent and self-stabilizing under unfair daemon.

Stabilization time is polynomial in moves and optimal in rounds.

Results apply to various existing algorithms in spanning forest networks.

Abstract

In this paper, we formalize design patterns, commonly used in the self-stabilizing area, to obtain general statements regarding both correctness and time complexity guarantees. Precisely, we study a general class of algorithms designed for networks endowed with a sense of direction describing a spanning forest (e.g., a directed tree or a network where a directed spanning tree is available) whose characterization is a simple (i.e., quasi-syntactic) condition. We show that any algorithm of this class is (1) silent and self-stabilizing under the distributed unfair daemon, and (2) has a stabilization time which is polynomial in moves and asymptotically optimal in rounds. To illustrate the versatility of our method, we review several existing works where our results apply.