Conference Paper
Deterministic HistoryIndependent Strategies for Storing Information on WriteOnce Memories.
Conference: Automata, Languages and Programming, 34th International Colloquium, ICALP 2007, Wroclaw, Poland, July 913, 2007, Proceedings
Source: DBLP

Chapter: Optimal Monotone Encodings
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ABSTRACT: 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 tamperproof data structures and arise also in the design of broadcast schemes in certain communication networks. To answer this question, we develop a relaxation of ksuperimposed families, which we call αfraction kmultiuser 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 2logn + O(1), which is optimal up to an additive constant.06/2008: pages 258270;  [Show abstract] [Hide abstract]
ABSTRACT: A (d,ℓ)list disjunct matrix is a nonadaptive group testing primitive which, given a set of items with at most d “defectives,” outputs a superset of the defectives containing less than ℓ nondefective 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 errortolerant list disjunct matrices which can correct up to e 0 false positive and e 1 false negative tests in sublinear time. We then use listdisjunct 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(dlog(n/d) + e 0 + de 1) 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 blackbox manner into errortolerant list disjunct matrices that are also efficiently decodable. The methods help us derive a family of (strongly) explicit constructions of listdisjunct matrices which are either optimal or near optimal, and which are also efficiently decodable. (3) We show how to use errorcorrecting efficiently decodable listdisjunct matrices in three different applications: (i) explicit constructions of ddisjunct matrices with t = O(d 2logn + 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(dlogn), and even for r = 0 this result improves upon known results; (ii) (explicit) constructions of (near)optimal, errorcorrecting, and efficiently decodable monotone encodings; and (iii) (explicit) constructions of (near)optimal, errorcorrecting, and efficiently decodable multiple user tracing families.01/2011; 
Conference Paper: Towards Tamperevident Storage on Patterned Media.
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ABSTRACT: We propose a tamperevident storage system based on probe storage with a patterned magnetic medium. This medium supports normal read/write operations by outofplane magnetisation of individual magnetic dots. We report on measurements showing that in principle the medium also supports a separate class of writeonce operation that destroys the outofplane magnetisation property of the dots irreversibly by precise local heating. We discuss the main issues of designing a tamperevident storage device and file system using the properties of the medium.6th USENIX Conference on File and Storage Technologies, FAST 2008, February 2629, 2008, San Jose, CA, USA; 01/2008
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