[Paper Review] Community aware group testing

Pavlos Nikolopoulos, Tao Guo+3 more|arXiv (Cornell University)|Jul 16, 2020

SARS-CoV-2 detection and testing4 citations

TL;DR

This paper proposes community-aware group testing algorithms that leverage known community structures—such as families or workgroups—to reduce the number of tests needed for identifying infected individuals. By designing adaptive and non-adaptive testing strategies that account for community-level infection correlations, the approach achieves significant test savings, especially in high-prevalence regimes, and improves reliability under noisy testing conditions using a novel loopy belief propagation decoder.

ABSTRACT

In this paper, we propose algorithms that leverage a known community structure to make group testing more efficient. We consider a population organized in disjoint communities: each individual participates in a community, and its infection probability depends on the community (s)he participates in. Use cases include families, students who participate in several classes, and workers who share common spaces. Group testing reduces the number of tests needed to identify the infected individuals by pooling diagnostic samples and testing them together. We show that if we design the testing strategy taking into account the community structure, we can significantly reduce the number of tests needed for adaptive and non-adaptive group testing, and can improve the reliability in cases where tests are noisy.

Motivation & Objective

• To address the inefficiency of traditional group testing in high-infection-prevalence regimes where k grows linearly with n.
• To exploit known community structures—such as families or shared workspaces—where infection spread is correlated within groups.
• To reduce the number of group tests required for identifying infected individuals by incorporating community-level infection patterns into test design.
• To improve reliability in noisy testing environments by integrating community structure into decoding, particularly using loopy belief propagation.
• To demonstrate that community-aware strategies outperform standard group testing in both sparse and linear infection regimes

Proposed method

• Proposes a lower bound on the number of tests that scales with the number of infected families (kf) rather than the number of infected individuals (k), reflecting community-level correlations.
• Introduces an adaptive algorithm that achieves the theoretical lower bound in certain parameter regimes by testing entire families first and then applying group testing within infected families.
• Develops a non-adaptive algorithm using a community-aware test matrix (C-encoder) that reduces test count when a small false positive rate is tolerable.
• Designs a generic loopy belief propagation (LBP) decoder that incorporates community structure via auxiliary nodes (Vj) in the factor graph, enabling compatibility with any test matrix.
• Employs a two-stage decoding process in non-adaptive settings: first identify infected families using a COMP-like decoder, then refine individual-level inference using LBP with community priors.
• Uses a Z-channel noise model to simulate false negative errors and evaluates performance under test noise, showing that community-aware LBP reduces false negatives significantly

Experimental results

Research questions

• RQ1 Can leveraging community structure in group testing reduce the number of tests required, especially when infection prevalence is high?
• RQ2 How does the number of infected families (kf) compare to the number of infected individuals (k) as a scaling parameter for test complexity in community-aware group testing?
• RQ3 Can non-adaptive group testing with community-aware encoding achieve lower error rates than standard non-adaptive methods, particularly when false positives are tolerated?
• RQ4 To what extent does incorporating community structure into the LBP decoder improve reliability in noisy testing environments?
• RQ5 How does the performance of community-aware group testing compare to traditional group testing in both sparse and linear infection regimes?

Key findings

• The proposed adaptive algorithm achieves the theoretical lower bound on the number of tests in specific parameter regimes, demonstrating optimality under community-aware design.
• In the linear infection regime (p > 0.5), community-aware non-adaptive group testing reduces error rates by up to 8.5% compared to traditional non-adaptive methods, with the gap increasing at higher prevalence.
• The LBP decoder with community structure (C-LBP) achieves near-zero false positive and false negative rates when p ≥ 0.6 and T > 450, outperforming the COMP decoder with C-encoder which saturates at a 2% false positive rate.
• Under noisy testing with Z-channel (z=0.15), community-aware LBP reduces false negative rates by up to 60% when test counts are low, significantly improving safety in real-world applications.
• In the asymmetric linear regime with 5% false negatives, Algorithm 1 with R=M reduces test count to 1.19× the probabilistic lower bound, compared to 6.19× for the baseline binary splitting algorithm (BSA), showing strong cost efficiency.
• The community-aware approach transforms a linear-regime problem into a sparse one by identifying and removing entire infected families early, thereby reducing the effective number of infected individuals and enabling group testing benefits