Enhancing Binary Search via Overlapping Partitions

2025-04-29

AI Summary

This paper addresses the severe error propagation and the difficulty of jointly optimizing error probability and search complexity in binary search under noisy conditions. We propose a robust search framework based on tunable overlapping partitions, which introduces controllable redundant intervals at each partitioning step. Our approach explicitly models the relationship between misclassification probability—under both discrete and continuous domains—and search depth, overcoming the limitations of conventional algorithms that provide only asymptotic guarantees or lack joint error–complexity control. Theoretical analysis quantifies the trade-off between overlap parameter, error rate, and search depth. Experiments demonstrate that the framework significantly improves robustness and convergence efficiency in localizing target regions under noisy measurements, establishing a new paradigm for noise-aware search. (136 words)

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Search
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Applications of semantic technologies for improving search, browsing, recommendation, personalization

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.

Problem

• Improving binary search robustness under noisy conditions
• Balancing error probability and search complexity trade-offs
• Enhancing target localization via tunable overlapping partitions

Innovation

• Introduces tunable overlapping partitions for binary search
• Balances error probability and search complexity explicitly
• Analyzes overlap impact on tree depth and errors