Existence of optimal <i>N</i>-slinky-turn-spiral search paths for finding <i>N</i>-dimensional Brownian target

Abstract

This paper presents more effective search technique for finding the N-dimensional Brownian target in N-dimensional space by using N-searchers. Each searcher moves along slinky-turn-spiral curve and starts its motion from the origin. An adaptive geometric features such as curvature and torsion of each searching path to meet the target is proposed. Rather than showing the existence of finite and optimal search paths, we find these optimal search paths which minimise the expected value of the first meeting time between one of the searchers and the target based on its geometric characteristics and features. A simulation study has been discussed to demonstrate the applicability of this technique.