Improved Bounds For Efficiently Decodable Probabilistic Group Testing With Unreliable Items.

This work uses non-adaptive probabilistic group testing to find a set of L defective items out of n items. In contrast to traditional group testing, in the considered setup each item can hide itself (or become inactive) during any given test with probability 1 - alpha and is active with probability alpha. The authors of [Cheraghchi et al.] proposed an efficiently decodable probabilistic group testing scheme which requires O (L log(n)/alpha(3))tests for the per-instance scenario (where the group testing matrix works for any arbitrary, but fixed, set of L defective items) and O(L-2 log(n/L)/alpha(3)) tests for the universal scenario (where the same group testing matrix works for all possible defective sets of L items). The contribution of this work is two-fold: (i) with a slight modification in the construction of the group testing matrix proposed by [Cheraghchi et al.], the corresponding bounds on the number of sufficient tests are improved to O(L log(n)/alpha(2)) and O(L-2 log(n/L)/alpha(2)) for the per-instance and universal scenarios respectively, while still using their efficient decoding method; and (ii) it is shown that the same bounds also hold for the fixed poolsize probabilistic group testing scenario, where in every test a fixed number of items are included for testing.