Communication Efficiency in Self-stabilizing Silent Protocols

TL;DR

This paper investigates communication efficiency in self-stabilizing protocols, proposing new measures, proving lower bounds for certain problems, and presenting protocols that minimize communication in the stabilized phase.

Contribution

It introduces new complexity measures, establishes lower bounds for communication in key problems, and designs protocols with reduced communication in the stabilized phase.

Findings

Communication complexity measures for stabilized phase

Impossibility results for minimal communication in certain problems

Protocols achieving low communication in stabilized phase

Abstract

Self-stabilization is a general paradigm to provide forward recovery capabilities to distributed systems and networks. Intuitively, a protocol is self-stabilizing if it is able to recover without external intervention from any catastrophic transient failure. In this paper, our focus is to lower the communication complexity of self-stabilizing protocols \emph{below} the need of checking every neighbor forever. In more details, the contribution of the paper is threefold: (i) We provide new complexity measures for communication efficiency of self-stabilizing protocols, especially in the stabilized phase or when there are no faults, (ii) On the negative side, we show that for non-trivial problems such as coloring, maximal matching, and maximal independent set, it is impossible to get (deterministic or probabilistic) self-stabilizing solutions where every participant communicates with less than every neighbor in the stabilized phase, and (iii) On the positive side, we present protocols for coloring, maximal matching, and maximal independent set such that a fraction of the participants communicates with exactly one neighbor in the stabilized phase.