Correction to "An asymptotically nonadaptive algorithm for conflict resolution i
IEEE Transactions on Information Theory
Explicit construction of exponential sized families of K-independent sets
Discrete Mathematics
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
Randomness conductors and constant-degree lossless expanders
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
European Journal of Combinatorics - Special issue on extremal and probabilistic combinatorics
Unbalanced Expanders and Randomness Extractors from Parvaresh-Vardy Codes
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Single-user tracing and disjointly superimposed codes
IEEE Transactions on Information Theory
Tracing Many Users With Almost No Rate Penalty
IEEE Transactions on Information Theory
Deterministic history-independent strategies for storing information on write-once memories
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Superselectors: efficient constructions and applications
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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
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Moran, Naor, and Segev have asked what is the minimal r = r(n, k) for which there exists an (n, k)-monotone encoding of length r, i.e., a monotone injective function from subsets of size up to k of {1, 2,..., n} to r bits. Monotone encodings are relevant to the study of tamper-proof data structures and arise also in the design of broadcast schemes in certain communication networks. To answer this question, we develop a relaxation of k-superimposed families, which we call α-fraction k-multiuser tracing (k, α)-FUT (fraction user-tracing) families). We show that r(n, k) = Θ(klog(n/k)) by proving tight asymptotic lower and upper bounds on the size of (k, α)-FUT families and by constructing an (n, k)-monotone encoding of length O(k log (n/k)). We also present an explicit construction of an (n, 2)-monotone encoding of length 2logn + O(1), which is optimal up to an additive constant.