# Optimal random search for a single hidden target - Physics > Data Analysis, Statistics and Probability

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

Author: ** Joseph Snider**

Source: https://arxiv.org/