Optimal network topologies for local search with congestion

TL;DR

This paper develops a formalism to analyze search efficiency and congestion in decentralized networks, identifying optimal topologies for different levels of parallel searches.

Contribution

It introduces a formalism that accounts for search and congestion effects, and determines optimal network structures for local search algorithms.

Findings

Star-like networks are optimal for few parallel searches.

Homogeneous-isotropic networks are optimal for many parallel searches.

The formalism provides expressions for average search cost with and without congestion.

Abstract

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.