3 research outputs found
A Fast Binary Splitting Approach to Non-Adaptive Group Testing
In this paper, we consider the problem of noiseless non-adaptive group
testing under the for-each recovery guarantee, also known as probabilistic
group testing. In the case of items and defectives, we provide an
algorithm attaining high-probability recovery with scaling in
both the number of tests and runtime, improving on the best known runtime previously available for any algorithm that only uses
tests. Our algorithm bears resemblance to Hwang's adaptive
generalized binary splitting algorithm (Hwang, 1972); we recursively work with
groups of items of geometrically vanishing sizes, while maintaining a list of
"possibly defective" groups and circumventing the need for adaptivity. While
the most basic form of our algorithm requires storage, we also
provide a low-storage variant based on hashing, with similar recovery
guarantees.Comment: Accepted to RANDOM 202