Graph-Aware Group Testing with Locally Clustered Infections

Group testing has been widely used to identify infected individuals with a limited number of tests, typically under the assumption of independent infections. Recent studies have exploited correlations among individuals, but often require additional information beyond the contact graph, such as community structures, interaction strengths, or detailed infection dynamics. Such information may be unavailable, incomplete or unreliable in practice. In this work, we assume that only the contact graph is known and develop a graph-aware group testing framework that exploits localized infection clustering in pooling design, fundamental limits of recovery, and decoding. Specifically, we propose an optimal transport-based pooling design that incorporates graph proximity and pooling constraints into a unified optimization framework. We prove that, under mild conditions, the proposed design eliminates uninfected individuals with higher probability than the Bernoulli pooling design, reducing the feasible search space for decoding. Then, we characterize the family of possible infected sets induced by localized infection clustering and derive necessary conditions on the number of tests required for exact recovery, revealing a lower testing requirement than that under the combinatorial prior. For decoding, we model the infection states of the population as a piecewise-constant graph signal and propose a graph total variation regularized decoder. We establish sufficient conditions for exact recovery under the Bernoulli pooling design in both noiseless and noisy settings, and show that O(Klog(n/K)) tests are sufficient under mild conditions in the noiseless case. Extensive simulations on synthetic and real-world networks demonstrate the effectiveness of the proposed framework and the benefit of exploiting graph-induced correlations in group testing.