Sparsity-Constrained Community-Based Group Testing

In this work, we consider the sparsity-constrained community-based group testing problem, where the population follows a community structure. In particular, the community consists of
$F$
families, each with
$M$
members. A number
$k_{f}$
out of the
$F$
families are infected, and a family is said to be infected if
$k_{m}$
out of its
$M$
members are infected. Furthermore, the sparsity constraint allows at most
$\rho_{T}$
individuals to be grouped in each test. For this sparsity-constrained community model, we propose a probabilistic group testing algorithm that can identify the infected population with a vanishing probability of error and we provide an upper-bound on the number of tests. When
$k_{m}=\Theta(M)$
and
$M=\omega(\log(FM))$
, our bound outperforms the existing sparsity-constrained group testing results trivially applied to the community model. If the sparsity constraint is relaxed, our achievable bound reduces to existing bounds for community-based group testing. Moreover, our scheme can also be applied to the classical dilution model, where it outperforms existing noise-level-independent schemes in the literature.