Near-Optimal Compressive Binary Search

TL;DR

This paper introduces a simple modification to compressive binary search that removes a suboptimal factor, achieving near-optimal performance in terms of SNR requirements and demonstrating improved practical results.

Contribution

The paper presents a modification to existing compressive binary search algorithms that enhances their optimality and practical performance.

Findings

The modified algorithm removes the log log n factor from SNR requirements.

Simulations confirm significant practical performance improvements.

The approach is contrasted with noisy binary search, highlighting differences.

Abstract

We propose a simple modification to the recently proposed compressive binary search. The modification removes an unnecessary and suboptimal factor of log log n from the SNR requirement, making the procedure optimal (up to a small constant). Simulations show that the new procedure performs significantly better in practice as well. We also contrast this problem with the more well known problem of noisy binary search.