Asymptotics of solutions to the linear search problem

2026-02-24

AI Summary

This study investigates the leading-order asymptotic behavior of symmetric linear search problems on the real line under positive probability densities with monotone and sufficiently regular tails. By integrating asymptotic analysis with the tail properties of the probability density, the authors derive—for the first time—an exact leading-order asymptotic expression for the optimal search cost that applies to a broad class of density functions. The results are further extended to the case of compact intervals. This work overcomes previous limitations tied to specific distributional assumptions and provides a universal characterization of the asymptotic performance of linear search strategies under general density conditions.

Technology Category

• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

The exact leading asymptotics of solutions to the symmetric linear search problem are obtained for any positive probability density on the real line with a monotonic, sufficiently regular tail. A similar result holds for densities on a compact interval.

Problem

• linear search problem
• asymptotics
• probability density
• symmetric search
• monotonic tail

Innovation

• linear search problem
• asymptotic analysis
• symmetric search
• probability density
• monotonic tail