Global consensus emergence in an unstructured semantic network

A global semantic consensus can emerge from the self-organization of a population of distributed agents connected through some communication network and playing local collaborative games: in a recently proposed class of self-organizing Semantic Overlay Networks, inspired by the mechanics of the Ising spin model, the condition which grants the convergence to a global consensus (Representative Agent condition -- of everyone knowing about the state of everybody else) is approximated by an equivalent uniform sampling over the nodes. In this way a specific mapping from a set of symbols to a set of concepts can become a shared convention for a set of peers. However uniform sampling is a non-trivial issue in unstructured overlays: one of the main hurdles to an homogeneous information dissemination in a random network is represented by topological bottlenecks. Relevant examples of such obstructions are network-graph bridges: they have a straightforward characterization, in terms of network reliability, as links whose failure makes the graph disconnected, i.e. broken in two non mutually reachable components; regions of a graph connected by a bridge are called pseudo-components. Messages failing to cross a bridge can prevent the information from one pseudo-component to reach another pseudo-component: in such conditions different pseudo-components can settle on a consensus state on their own, which does not correspond to a global consensus. In this paper we describe a distributed algorithm that improves the mutual reachability of any pair of nodes in an unstructured network of arbitrary topology, so that each agent can potentially disseminate its own state more uniformly to all the components of the network: the algorithm is based on a self-establishing gradient mechanism and bears some similarity to algorithms such as the ant-colony algorithms.