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- W2286685332 abstract "A (d,ℓ)-list disjunct matrix is a non-adaptive group testing primitive which, given a set of items with at most d “defectives,” outputs a superset of the defectives containing less than ℓ non-defective items. The primitive has found many applications as stand alone objects and as building blocks in the construction of other combinatorial objects. This paper studies error-tolerant list disjunct matrices which can correct up to e 0 false positive and e 1 false negative tests in sub-linear time. We then use list-disjunct matrices to prove new results in three different applications. Our major contributions are as follows. (1) We prove several (almost)-matching lower and upper bounds for the optimal number of tests, including the fact that Θ(dlog(n/d) + e 0 + de 1) tests is necessary and sufficient when ℓ = Θ(d). Similar results are also derived for the disjunct matrix case (i.e. ℓ = 1). (2) We present two methods that convert error-tolerant list disjunct matrices in a black-box manner into error-tolerant list disjunct matrices that are also efficiently decodable. The methods help us derive a family of (strongly) explicit constructions of list-disjunct matrices which are either optimal or near optimal, and which are also efficiently decodable. (3) We show how to use error-correcting efficiently decodable list-disjunct matrices in three different applications: (i) explicit constructions of d-disjunct matrices with t = O(d 2logn + rd) tests which are decodable in poly(t) time, where r is the maximum number of test errors. This result is optimal for r = Ω(dlogn), and even for r = 0 this result improves upon known results; (ii) (explicit) constructions of (near)-optimal, error-correcting, and efficiently decodable monotone encodings; and (iii) (explicit) constructions of (near)-optimal, error-correcting, and efficiently decodable multiple user tracing families." @default.
- W2286685332 created "2016-06-24" @default.
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- W2286685332 date "2011-01-01" @default.
- W2286685332 modified "2023-10-05" @default.
- W2286685332 title "Efficiently Decodable Error-Correcting List Disjunct Matrices and Applications" @default.
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- W2286685332 doi "https://doi.org/10.1007/978-3-642-22006-7_47" @default.
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