Optimal random search for a single hidden target

Abstract

A single target is hidden at a location chosen from a predetermined probability distribution. Then, a searcher must find a second probability distribution from which random search points are sampled such that the target is found in the minimum number of trials. Here it will be shown that if the searcher must get very close to the target to find it, then the best search distribution is proportional to the square root of the target distribution. For a Gaussian target distribution, the optimum search distribution is approximately a Gaussian with a standard deviation that varies inversely with how close the searcher must be to the target to find it. For a network, where the searcher randomly samples nodes and looks for the fixed target along edges, the optimum is to either sample a node with probability proportional to the square root of the out degree plus one or not at all.

13 pages, 5 figures

References in corpus (2)

• Finding community structure in networks using the eigenvectors of matrices
• Kinetics of protein-DNA interaction: facilitated target location in sequence-dependent potential

Cited by in corpus (8)

• Stochastic Resetting and Applications
• Diffusion with Optimal Resetting
• Statistical patterns of visual search for hidden objects
• Non-linear diffusion with stochastic resetting
• Searching for clusters of targets under stochastic resetting
• Optimal potentials for diffusive search strategies
• Stochastic resetting prevails over sharp restart for broad target distributions
• Levy flights in confining environments: Random paths and their statistics