On the upper bound of the size of the r-cover-free families
Journal of Combinatorial Theory Series A
Journal of Combinatorial Theory Series A
Explicit constructions of selectors and related combinatorial structures, with applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
What's hot and what's not: tracking most frequent items dynamically
ACM Transactions on Database Systems (TODS) - Special Issue: SIGMOD/PODS 2003
Optimal Two-Stage Algorithms for Group Testing Problems
SIAM Journal on Computing
Correcting Errors Beyond the Guruswami-Sudan Radius in Polynomial Time
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Explicit Non-adaptive Combinatorial Group Testing Schemes
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Data Stream Algorithms via Expander Graphs
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
IEEE Transactions on Information Theory
Noise-resilient group testing: limitations and constructions
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Efficiently decodable non-adaptive group testing
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Data stream algorithms for codeword testing
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Indexing information for data forensics
ACNS'05 Proceedings of the Third international conference on Applied Cryptography and Network Security
Tracing Many Users With Almost No Rate Penalty
IEEE Transactions on Information Theory
Noise-resilient group testing: Limitations and constructions
Discrete Applied Mathematics
Homomorphic fingerprints under misalignments: sketching edit and shift distances
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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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 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, including the fact that Θ(d log(n/d) + e0+ de1) 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 errortolerant 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 log n+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(d log n), 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.