Enhancing Binary Search via Overlapping Partitions

Abstract: This paper considers the task of performing binary search under noisy decisions, focusing on the application of target area localization. In the presence of noise, the classical partitioning approach of binary search is prone to error propagation due to the use of strictly disjoint splits. While existing works on noisy binary search propose techniques such as query repetition or probabilistic updates to mitigate errors, they often lack explicit mechanisms to manage the trade-off between error probability and search complexity, with some providing only asymptotic guarantees. To address this gap, we propose a binary search framework with tunable overlapping partitions, which introduces controlled redundancy into the search process to enhance robustness against noise. We analyze the performance of the proposed algorithm in both discrete and continuous domains for the problem of area localization, quantifying how the overlap parameter impacts the trade-off between search tree depth and error probability. Unlike previous methods, this approach allows for direct control over the balance between reliability and efficiency. Our results emphasize the versatility and effectiveness of the proposed method, providing a principled extension to existing noisy search paradigms and enabling new insights into the interplay between partitioning strategies and measurement reliability.