Average search time bound in cue based search strategy

TL;DR

This paper derives lower bounds on the average search time for cue-based search strategies that utilize past information, including a specific case for homogeneous diffusion, highlighting the exponential relation with entropy.

Contribution

It provides a novel lower bound for search time in cue-based strategies and extends the analysis to general probability distributions with entropy considerations.

Findings

Lower bound for search time derived for a specific strategy.

Analytic expression for the lower bound in homogeneous diffusion case.

Lower bound scales as exp(E/2) for entropy E.

Abstract

In this work we consider the problem of searches that utilises past information gathered during searching, to evaluate the probability distribution of finding the source at each step. We start with a sample strategy where the movement at each step is in the immediate neighbourhood direction, with a probability proportional to the normalised difference in probability of finding the source with the present position source finding probability. We evaluate a lower bound for the average search time for this strategy . We next consider the problem of the lowerbound on any strategy that utilities information of the probability distribution evaluated by the searcher at any instant. We derive an expression for the same. Finally we present an analytic expression for this lower bound in the case of homogeneous diffusion of particles by a source. For a general probability distribution with entropy-E, we find that the lower bound goes as exp(E/2).