TY - GEN

T1 - Optimal monotone encodings

AU - Alon, Noga

AU - Hod, Rani

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2008

Y1 - 2008

N2 - 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-multi-user tracing ((k, α)-FUT families). We show that r(n, k) = Θ(k log(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 2log n + O(1), which is optimal up to an additive constant.

AB - 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-multi-user tracing ((k, α)-FUT families). We show that r(n, k) = Θ(k log(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 2log n + O(1), which is optimal up to an additive constant.

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U2 - 10.1007/978-3-540-70575-8_22

DO - 10.1007/978-3-540-70575-8_22

M3 - Conference contribution

AN - SCOPUS:49049086517

SN - 3540705740

SN - 9783540705741

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 258

EP - 270

BT - Automata, Languages and Programming - 35th International Colloquium, ICALP 2008, Proceedings

T2 - 35th International Colloquium on Automata, Languages and Programming, ICALP 2008

Y2 - 7 July 2008 through 11 July 2008

ER -