Search on the Brink of Chaos

TL;DR

This paper explores the classical linear search problem through Hamiltonian dynamics, revealing that the optimal search strategy aligns with an unstable separatrix in the system for exponentially distributed targets.

Contribution

It introduces a novel dynamical systems perspective to the linear search problem, identifying the optimal plan as following an unstable separatrix in the Hamiltonian framework.

Findings

Optimal search follows an unstable separatrix.

Hamiltonian dynamics provides new insights into search strategies.

Results specific to exponential distribution of target location.

Abstract

The classical linear search problem is studied from the view point of Hamiltonian dynamics. For the specific, yet representative case of exponentially distributed position of the hidden object, we show that the optimal plan follows an unstable separatrix which is present in the associated Hamiltonian system.