Improved group testing rates with constant column weight designs

Abstract

We consider nonadaptive group testing where each item is placed in a constant number of tests. The tests are chosen uniformly at random with replacement, so the testing matrix has (almost) constant column weights. We show that performance is improved compared to Bernoulli designs, where each item is placed in each test independently with a fixed probability. In particular, we show that the rate of the practical COMP detection algorithm is increased by 31% in all sparsity regimes. In dense cases, this beats the best possible algorithm with Bernoulli tests, and in sparse cases is the best proven performance of any practical algorithm. We also give an algorithm-independent upper bound for the constant column weight case; for dense cases this is again a 31% increase over the analogous Bernoulli result.

5 pages, 2 figures; to be presented at ISIT 2016

References in corpus (2)

• Group testing with Random Pools: Phase Transitions and Optimal Strategy
• Strong converses for group testing in the finite blocklength regime

Cited by in corpus (5)

• Performance of group testing algorithms with near-constant tests-per-item
• Information-theoretic and algorithmic thresholds for group testing
• Improved bounds for noisy group testing with constant tests per item
• Near optimal sparsity-constrained group testing: improved bounds and algorithms
• Nearly Optimal Sparse Group Testing