Efficiently Decodable Non-adaptive Group Testing

We consider the following "efficiently decodable" nonadaptive group testing problem. There is an unknown string x {0, 1}n with at most d ones in it. We are allowed to test any subset S [n] of the indices. The answer to the test tells whether xi = 0 for all i S or not. The objective is to design as few tests as possible (say, t tests) such that x can be identified as fast as possible (say, poly(t)-time). Efficiently decodable non-adaptive group testing has applications in many areas, including data stream algorithms and data forensics. A non-adaptive group testing strategy can be represented by a t ? n matrix, which is the stacking of all the characteristic vectors of the tests. It is well-known that if this matrix is d-disjunct, then any test outcome corresponds uniquely to an unknown input string. Furthermore, we know how to construct d-disjunct matrices with t = O(d2 log n) efficiently. However, these matrices so far only allow for a "decoding" time of O(nt), ...

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: Piotr Indyk, Hung Q. Ngo, Atri Rudra
• Keywords: )-list Disjunct Matrices, Discrete Algorithms, List Disjunct Matrices, Log N, SODA 2010