Communication and optimal hierarchical networks

We study a general and simple model for communication processes. In the model, agents in a network (in particular, an organization) interchange information packets following simple rules that take into account the limited capability of the agents to deal with packets and the cost associated to the existence of open communication channels. Due to the limitation in the capability, the network collapses under certain conditions. We focus on when the collapse occurs for hierarchical networks and also on the influence of the flatness or steepness of the structure. We find that the need for hierarchy is related to the existence of costly connections.Comment: 7 pages, 2 figures. NATO ARW on Econophysic

Communication in networks with hierarchical branching

We present a simple model of communication in networks with hierarchical branching. We analyze the behavior of the model from the viewpoint of critical systems under different situations. For certain values of the parameters, a continuous phase transition between a sparse and a congested regime is observed and accurately described by an order parameter and the power spectra. At the critical point the behavior of the model is totally independent of the number of hierarchical levels. Also scaling properties are observed when the size of the system varies. The presence of noise in the communication is shown to break the transition. Despite the simplicity of the model, the analytical results are a useful guide to forecast the main features of real networks.Comment: 4 pages, 3 figures. Final version accepted in PR

Pricing in Social Networks with Negative Externalities

We study the problems of pricing an indivisible product to consumers who are embedded in a given social network. The goal is to maximize the revenue of the seller. We assume impatient consumers who buy the product as soon as the seller posts a price not greater than their values of the product. The product's value for a consumer is determined by two factors: a fixed consumer-specified intrinsic value and a variable externality that is exerted from the consumer's neighbors in a linear way. We study the scenario of negative externalities, which captures many interesting situations, but is much less understood in comparison with its positive externality counterpart. We assume complete information about the network, consumers' intrinsic values, and the negative externalities. The maximum revenue is in general achieved by iterative pricing, which offers impatient consumers a sequence of prices over time. We prove that it is NP-hard to find an optimal iterative pricing, even for unweighted tree networks with uniform intrinsic values. Complementary to the hardness result, we design a 2-approximation algorithm for finding iterative pricing in general weighted networks with (possibly) nonuniform intrinsic values. We show that, as an approximation to optimal iterative pricing, single pricing can work rather well for many interesting cases, but theoretically it can behave arbitrarily bad

Optimal network topologies for local search with congestion

The problem of searchability in decentralized complex networks is of great importance in computer science, economy and sociology. We present a formalism that is able to cope simultaneously with the problem of search and the congestion effects that arise when parallel searches are performed, and obtain expressions for the average search cost--written in terms of the search algorithm and the topological properties of the network--both in presence and abscence of congestion. This formalism is used to obtain optimal network structures for a system using a local search algorithm. It is found that only two classes of networks can be optimal: star-like configurations, when the number of parallel searches is small, and homogeneous-isotropic configurations, when the number of parallel searches is large.Comment: 4 pages. Final version accepted in PR