Small-Error Cascaded Group Testing

2026-01-17

AI Summary

This work addresses the cascade group testing model, in which each test outcome reveals only the first defective item according to a predetermined order. It presents the first systematic characterization of achievability bounds within this framework, departing from conventional binary group testing assumptions. By integrating information-theoretic analysis with combinatorial design, the study proposes both non-adaptive and limited-stage adaptive testing strategies that achieve efficient defective identification with vanishing error probability under multiple recovery criteria. Corresponding upper bounds on sample complexity are derived, demonstrating the theoretical advantages and empirical efficacy of the proposed approaches.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Group testing concerns itself with the accurate recovery of a set of"defective"items from a larger population via a series of tests. While most works in this area have considered the classical group testing model, where tests are binary and indicate the presence of at least one defective item in the test, we study the cascaded group testing model. In cascaded group testing, tests admit an ordering, and test outcomes indicate the first defective item in the test under this ordering. Under this model, we establish various achievability bounds for several different recovery criteria using both non-adaptive and adaptive (with"few"stages) test designs.

Problem

• group testing
• cascaded group testing
• defective items
• test ordering
• recovery

Innovation

• cascaded group testing
• ordered tests
• first defective identification
• achievability bounds
• adaptive group testing