Topology-dependent density optima for efficient simultaneous network exploration

TL;DR

This paper investigates how network topology influences the optimal number of concurrent searchers for efficient exploration, introducing the APCT metric and revealing that spectral gap predicts density optima, with bias further enhancing capacity.

Contribution

It introduces the APCT metric for parallel search efficiency and demonstrates how spectral gap and bias affect optimal searcher density in network exploration.

Findings

APCT quantifies parallel search efficiency in networks.

Spectral gap predicts optimal searcher density.

Bias increases the maximum sustainable searcher density.

Abstract

A random search process in a networked environment is governed by the time it takes to visit every node, termed the cover time. Often, a networked process does not proceed in isolation but competes with many instances of itself within the same environment. A key unanswered question is how to optimise this process: how many concurrent searchers can a topology support before the benefits of parallelism are outweighed by competition for space? Here, we introduce the searcher-averaged parallel cover time (APCT) to quantify these economies of scale. We show that the APCT of the networked symmetric exclusion process is optimised at a searcher density that is well predicted by the spectral gap. Furthermore, we find that non-equilibrium processes, realised through the addition of bias, can support significantly increased density optima. Our results suggest novel hybrid strategies of serial and parallel search for efficient information gathering in social interaction and biological transport networks.