3 research outputs found

    On a Hypergraph Approach to Multistage Group Testing Problems

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    Group testing is a well known search problem that consists in detecting up to ss defective elements of the set [t]={1,…,t}[t]=\{1,\ldots,t\} by carrying out tests on properly chosen subsets of [t][t]. In classical group testing the goal is to find all defective elements by using the minimal possible number of tests. In this paper we consider multistage group testing. We propose a general idea how to use a hypergraph approach to searching defects. For the case s=2s=2, we design an explicit construction, which makes use of 2log⁑2t(1+o(1))2\log_2t(1+o(1)) tests in the worst case and consists of 44 stages.Comment: ACCT 2016, 6 page

    A New Algorithm for Two-Stage Group Testing

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    Group testing is a well-known search problem that consists in detecting of ss defective members of a set of tt samples by carrying out tests on properly chosen subsets of samples. In classical group testing the goal is to find all defective elements by using the minimal possible number of tests in the worst case. In this work, two-stage group testing is considered. Using the hypergraph approach we design a new search algorithm, which allows improving the known results for fixed ss and tβ†’βˆžt\to\infty. For the case s=2s=2 this algorithm achieves information-theoretic lower bound 2log⁑2t(1+o(1))2\log_2t(1+o(1)) on the number of tests in the worst case. Also, the problem of finding mm out of ss defectives is considered.Comment: 7 pages, 1 tabl

    Optimal Multistage Group Testing Algorithm for 3 Defectives

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    Group testing is a well-known search problem that consists in detecting of ss defective members of a set of tt samples by carrying out tests on properly chosen subsets of samples. In classical group testing the goal is to find all defective elements by using the minimal possible number of tests in the worst case. In this work, a multistage group testing problem is considered. Our goal is to construct a multistage search procedure, having asymptotically the same number of tests as the optimal adaptive algorithm. We propose a new approach to designing multistage algorithms, which allows us to construct a 5-stage algorithm for finding 3 defectives with the optimal number 3log⁑2t(1+o(1))3\log_2t(1+o(1)) of tests
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