Improved lower bounds on k-independence
Journal of Graph Theory
Journal of Combinatorial Theory Series A
Efficient approximation of product distributions
Random Structures & Algorithms
A group testing method for finding patterns in data
Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
Finding Large Independent Sets in Graphs and Hypergraphs
SIAM Journal on Discrete Mathematics
What's hot and what's not: tracking most frequent items dynamically
ACM Transactions on Database Systems (TODS) - Special Issue: SIGMOD/PODS 2003
Correcting Errors Beyond the Guruswami-Sudan Radius in Polynomial Time
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Algorithmic construction of sets for k-restrictions
ACM Transactions on Algorithms (TALG)
Unbalanced Expanders and Randomness Extractors from Parvaresh-Vardy Codes
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Concatenated codes can achieve list-decoding capacity
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
List decoding and property testing of error-correcting codes
List decoding and property testing of error-correcting codes
Soft Decoding, Dual BCH Codes, and Better List-Decodable e-Biased Codes
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
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
Noise-resilient group testing: limitations and constructions
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Indexing information for data forensics
ACNS'05 Proceedings of the Third international conference on Applied Cryptography and Network Security
Linear diophantine equations over polynomials and soft decoding of Reed-Solomon codes
IEEE Transactions on Information Theory
Data stream algorithms for codeword testing
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Superselectors: efficient constructions and applications
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Non-adaptive complex group testing with multiple positive sets
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Efficiently decodable error-correcting list disjunct matrices and applications
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Noise-resilient group testing: Limitations and constructions
Discrete Applied Mathematics
Distributed sensor failure detection in sensor networks
Signal Processing
A variant of non-adaptive group testing and its application in pay-television via internet
ICT-EurAsia'13 Proceedings of the 2013 international conference on Information and Communication Technology
Testers and their applications
Proceedings of the 5th conference on Innovations in theoretical computer science
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We consider the following "efficiently decodable" non-adaptive group testing problem. There is an unknown string x ∈ {0, 1}n with at most d ones in it. We are allowed to test any subset S ⊆ [n] of the indices. The answer to the test tells whether xi = 0 for all i ∈ S or not. The objective is to design as few tests as possible (say, t tests) such that x can be identified as fast as possible (say, poly(t)-time). Efficiently decodable non-adaptive group testing has applications in many areas, including data stream algorithms and data forensics. A non-adaptive group testing strategy can be represented by a t x n matrix, which is the stacking of all the characteristic vectors of the tests. It is well-known that if this matrix is d-disjunct, then any test outcome corresponds uniquely to an unknown input string. Furthermore, we know how to construct d-disjunct matrices with t = O(d2 log n) efficiently. However, these matrices so far only allow for a "decoding" time of O(nt), which can be exponentially larger than poly(t) for relatively small values of d. This paper presents a randomness efficient construction of d-disjunct matrices with t = O(d2 log n) that can be decoded in time poly(d) · t log2 t + O(t2). To the best of our knowledge, this is the first result that achieves an efficient decoding time and matches the best known O(d2 log n) bound on the number of tests. We also derandomize the construction, which results in a polynomial time deterministic construction of such matrices when d = O(log n / log log n). A crucial building block in our construction is the notion of (d, l)-list disjunct matrices, which represent the more general "list group testing" problem whose goal is to output less than d + l positions in x, including all the (at most d) positions that have a one in them. List disjunct matrices turn out to be interesting objects in their own right and were also considered independently by [Cheraghchi, FCT 2009]. We present connections between list disjunct matrices, expanders, dispersers and disjunct matrices. List disjunct matrices have applications in constructing (d, l)-sparsity separator structures [Ganguly, ISAAC 2008] and in constructing tolerant testers for Reed-Solomon codes in the data stream model.