Optimal Searcher Distribution for Parallel Random Target Searches

Abstract

We consider a problem of finding a target located in a finite $d$-dimensional domain, using $N$ independent random walkers, when partial information on the target location is given as a probability distribution. When $N$ is large, the first-passage time sensitively depends on the initial searcher distribution, which invokes the question of what is the optimal searcher distribution that minimizes the first-passage time. Here, we analytically derive the equation for the optimal distribution and explore its limiting expressions. If the target volume can be ignored, the optimal distribution is proportional to the target distribution to the power of one-third. If we consider a target of a finite volume and the probability of initial overlapping of searchers with the target cannot be ignored in the large $N$ limit, the optimal distribution has a weak dependence on the target distribution, given as a logarithm of the target distribution. Using Langevin dynamics simulations, we numerically demonstrate our predictions in one- and two-dimensions.

7 pages, 3 figures

References in corpus (9)

• First-passage times in complex scale-invariant media
• First passages for a search by a swarm of independent random searchers
• Mortality, Redundancy, and Diversity in Stochastic Search
• Inverse square Lévy walks are not optimal search strategies for $d\ge 2$
• From single-particle stochastic kinetics to macroscopic reaction rates: fastest first-passage time of $N$ random walkers
• Optimal non-Markovian search strategies with n-step memory
• Lifetime of a target in the presence of N independent walkers
• Random walks with fractally correlated traps: Stretched exponential and power law survival kinetics
• Random Walks on Complex Networks

Cited by in corpus (1)

• Target Searches of Interacting Brownian Particles