Communication Efficiency in Self-Stabilizing Silent Protocols

In this paper, our focus is to lower the communication complexity of self-stabilizing protocols below the need of checking every neighbor forever. Our contribution 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 maximal matching and maximal independent set such that a fraction of the participants communicates with exactly one neighbor in the stabilized phase.