Mediated population protocols

Abstract

We extend here the Population Protocol model of Angluin et al. [2] in order to model more powerful networks of very small resource-limited artefacts (agents) that are possibly mobile. The main feature of our extended model is to allow edges of the communication graph, G, to have states that belong to a constant size set. We also allow edges to have readable only costs, whose values also belong to a constant size set. Our protocol specifications are still independent of the population size and do not use agent ids, i.e. they preserve uniformity and anonymity. Our Mediated Population Protocols (MPP) can stably compute graph properties of the communication graph. We show this for the properties of maximal matchings (in undirected communication graphs), also for finding the transitive closure of directed graphs and for finding all edges of small cost. We demonstrate that our mediated protocols are stronger than the classical population protocols, by presenting a MPP for a non-semilinear predicate. To show this fact, we state and prove a general theorem about the composition of two stably computing mediated population protocols. We also show that all predicates stably computable in our model are (non-uniformly) in the class NSPACE(|E(G)|). © 2009 Springer Berlin Heidelberg.