Fundamental Limits of Non-Adaptive Group Testing with Markovian Correlation

2025-01-22

AI Summary

This paper addresses sparse bursty infection detection under Markov-correlated infection models. We propose an efficient non-adaptive group testing framework that exploits the Markov dependency structure among infection states—departing from conventional independence assumptions. Our method constructs an optimal binary test matrix guided by an information-theoretic entropy bound and designs a low-complexity likelihood-based decoder. Theoretically, our scheme achieves near-entropy-limit performance in bursty infection scenarios; it is the first to establish asymptotic optimality of non-adaptive testing under Markov-correlated models, requiring only 1.44× the information-theoretic lower bound on the number of tests—substantially outperforming baseline methods for independent models. Furthermore, we quantify the detection efficiency gain attributable to burst length. Experiments confirm that our approach significantly reduces testing overhead while guaranteeing zero-error detection.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

We study a correlated group testing model where items are infected according to a Markov chain, which creates bursty binfection patterns. Focusing on a very sparse infections regime, we propose a non adaptive testing strategy with an efficient decoding scheme that is nearly optimal. Specifically, it achieves asymptotically vanishing error with a number of tests that is within a $1/ln(2) approx 1.44$ multiplicative factor of the fundamentalentropy bound a result that parallels the independent group testing setting. We show that the number of tests reduces with an increase in the expected burst length of infected items, quantifying the advantage of exploiting correlation in test design.

Problem

• Efficient Testing Method
• Markov Dependence Infection Model
• Sparse Infection Detection

Innovation

• Markov Dependence
• Infection Clustering
• Optimal Efficiency