986 research outputs found
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
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