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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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