DMCA
Efficiently decodable error-correcting list disjunct matrices and applications (Extended Abstract) (2011)
| Venue: | IN ICALP |
| Citations: | 3 - 0 self |
BibTeX
@INPROCEEDINGS{Ngo11efficientlydecodable,
author = {Hung Q. Ngo and Ely Porat and Atri Rudra},
title = {Efficiently decodable error-correcting list disjunct matrices and applications (Extended Abstract)},
booktitle = {IN ICALP},
year = {2011},
pages = {557--568},
publisher = {}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
A (d, `)-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 ` 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 e0 false positive and e1 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, in-cluding the fact that Θ(d log(n/d) + e0 + de1) tests is necessary and sufficient when ` = Θ(d). Similar results are also derived for the dis-junct matrix case (i.e. ` = 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(d2 logn+ rd) tests which are decodable in poly(t) time, where r is the maximum num-ber of test errors. This result is optimal for r = Ω(d logn), and even for r = 0 this result improves upon known results; (ii) (explicit) con-structions 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.
Keyphrases
decodable error-correcting list disjunct matrix different application error-tolerant list disjunct matrix list-disjunct matrix list disjunct matrix many application similar result dis-junct matrix case e1 false negative test building block non-adaptive group non-defective item decodable list-disjunct matrix major contribution explicit construction new result combinatorial object decodable multiple user maximum num-ber optimal number d-disjunct matrix test error d2 logn rd sub-linear time upper bound decodable monotone encoding black-box manner
