Lower Bounds for Identifying Subset Members with Subset Queries (1995)
| Citations: | 3 - 0 self |
BibTeX
@MISC{Knill95lowerbounds,
author = {E. Knill},
title = {Lower Bounds for Identifying Subset Members with Subset Queries},
year = {1995}
}
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Abstract
An instance of a group testing problem is a set of objects O and an unknown subset P of O. The task is to determine P by using queries of the type "does P intersect Q", where Q is a subset of O. This problem occurs in areas such as fault detection, multiaccess communications, optimal search, blood testing and chromosome mapping. Consider the two stage algorithm for solving a group testing problem. In the first stage a predetermined set of queries are asked in parallel and in the second stage, P is determined by testing individual objects. Let n = O . Suppose that P is generated by independently adding each x 2 O to P with probability p=n. Let q1 (q2) be the number of queries asked in the first (second) stage of this algorithm. We show that if q1 = o(log(n) log(n)= log log(n)), then Exp(q2) = n 1\Gammao(1) , while there exist algorithms with q1 = O(log(n) log(n)= log log(n)) and Exp(q2 ) = o(1). The proof involves a relaxation technique which can be used with arbitrary distributio...
