SAFFRON: A Fast, Efficient, and Robust Framework for Group Testing Based on Sparse-Graph Codes - Lee, Kangwook; Chandrasekher, Kabir; Pedarsani, Ramtin; Ramchandran, Kannan (IEEE transactions on signal processing, 2019)
Group testing is the problem of identifying K defective items among n items by pooling groups of items. In this paper, we design group testing algorithms for approximate recovery with order-optimal sample complexity by leveraging design and analysis tools from modern sparse-graph coding theory. Our algorithm, SAFFRON, recovers at least (1-ε)K defective items w.p. 1-K/n^r with m=2(1+r)C(ε)K\log _2{n} tests, where ε is an arbitrarily small constant, C(ε) is a precisely characterizable constant, and r is any positive integer. The decoding complexity is Θ (K\log n) . We also propose variations of SAFFRON, which are robust to noise and unknown offsets. For example, for n \simeq 4.3× 10^9 and K = 128 , our algorithm is observed to recover all defective items with m \simeq 8.3× 10^{5} tests, even in the presence of noisy test results. Moreover, the decoding time takes less than 4 seconds on a laptop with a 2 GHz Intel Core i7 and 8 GB memory.