Efficient designs for threshold group testing without gap
CoRR(2024)
Abstract
Given d defective items in a population of n items with d ≪ n, in
threshold group testing without gap, the outcome of a test on a subset of items
is positive if the subset has at least u defective items and negative
otherwise, where 1 ≤ u ≤ d. The basic goal of threshold group testing
is to quickly identify the defective items via a small number of tests. In
non-adaptive design, all tests are designed independently and can be performed
in parallel. The decoding time in the non-adaptive state-of-the-art work is a
polynomial of (d/u)^u (d/(d-u))^d - u, d, and logn. In this work, we
present a novel design that significantly reduces the number of tests and the
decoding time to polynomials of min{u^u, (d - u)^d - u}, d, and
logn. In particular, when u is a constant, the number of tests and the
decoding time are O(d^3 (log^2n) log(n/d) ) and O(d^3 (log^2n)
log(n/d) + d^2 (logn) log^3(n/d)), respectively. For a special
case when u = 2, with non-adaptive design, the number of tests and the
decoding time are O(d^3 (logn) log(n/d) ) and O(d^2 (logn +
log^2(n/d)) ), respectively. Moreover, with 2-stage design, the number of
tests and the decoding time are O(d^2 log^2(n/d) ).
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