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168
Revealing information while preserving privacy
 In PODS
, 2003
"... We examine the tradeoff between privacy and usability of statistical databases. We model a statistical database by an nbit string d1,.., dn, with a query being a subset q ⊆ [n] to be answered by � i∈q di. Our main result is a polynomial reconstruction algorithm of data from noisy (perturbed) subset ..."
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Cited by 199 (10 self)
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We examine the tradeoff between privacy and usability of statistical databases. We model a statistical database by an nbit string d1,.., dn, with a query being a subset q ⊆ [n] to be answered by � i∈q di. Our main result is a polynomial reconstruction algorithm of data from noisy (perturbed) subset sums. Applying this reconstruction algorithm to statistical databases we show that in order to achieve privacy one has to add perturbation of magnitude Ω ( √ n). That is, smaller perturbation always results in a strong violation of privacy. We show that this result is tight by exemplifying access algorithms for statistical databases that preserve privacy while adding perturbation of magnitude Õ(√n). For timeT bounded adversaries we demonstrate a privacypreserving access algorithm whose perturbation magnitude is ≈ √ T. 1
Expander Graphs and their Applications
, 2003
"... Contents 1 The Magical Mystery Tour 7 1.1 Some Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.1 Hardness results for linear transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.2 Error Correcting Codes . . . . . . . ..."
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Cited by 188 (5 self)
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Contents 1 The Magical Mystery Tour 7 1.1 Some Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.1 Hardness results for linear transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.2 Error Correcting Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.3 Derandomizing Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Magical Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.1 A Super Concentrator with O(n) edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.2 Error Correcting Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.3 Derandomizing Random Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
On the SumofSquares algorithms for bin packing
, 2006
"... In this article we present a theoretical analysis of the online SumofSquares algorithm (SS) for bin packing along with several new variants. SS is applicable to any instance of bin packing in which the bin capacity B and item sizes s(a) are integral (or can be scaled to be so), and runs in time ..."
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Cited by 108 (7 self)
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In this article we present a theoretical analysis of the online SumofSquares algorithm (SS) for bin packing along with several new variants. SS is applicable to any instance of bin packing in which the bin capacity B and item sizes s(a) are integral (or can be scaled to be so), and runs in time O(nB). It performs remarkably well from an average case point of view: For any discrete distribution in which the optimal expected waste is sublinear, SS also has sublinear expected waste. For any discrete distribution where the optimal expected waste is bounded, SS has expected waste at most O(log n). We also discuss several interesting variants on SS, including a randomized O(nBlog B)time online algorithm SS ∗ whose expected behavior is essentially optimal for all discrete distributions. Algorithm SS ∗ depends on a new linearprogrammingbased pseudopolynomialtime algorithm for solving the
ChernoffHoeffding Bounds for Applications with Limited Independence
 SIAM J. Discrete Math
, 1993
"... ChernoffHoeffding bounds are fundamental tools used in bounding the tail probabilities of the sums of bounded and independent random variables. We present a simple technique which gives slightly better bounds than these, and which more importantly requires only limited independence among the rando ..."
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Cited by 104 (10 self)
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ChernoffHoeffding bounds are fundamental tools used in bounding the tail probabilities of the sums of bounded and independent random variables. We present a simple technique which gives slightly better bounds than these, and which more importantly requires only limited independence among the random variables, thereby importing a variety of standard results to the case of limited independence for free. Additional methods are also presented, and the aggregate results are sharp and provide a better understanding of the proof techniques behind these bounds. They also yield improved bounds for various tail probability distributions and enable improved approximation algorithms for jobshop scheduling. The "limited independence" result implies that a reduced amount of randomness and weaker sources of randomness are sufficient for randomized algorithms whose analyses use the ChernoffHoeffding bounds, e.g., the analysis of randomized algorithms for random sampling and oblivious packet routi...
Hardness of approximating the shortest vector problem in high Lp norms
 In Proceedings of the 44th IEEE Symposium on Foundations of Computer Science. IEEE Computer
"... Abstract. Let p> 1beany fixed real. We show that assuming NP ⊆ RP, there is no polynomial time algorithm that approximates the Shortest Vector Problem (SVP) in ℓp norm within a constant factor. Under the stronger assumption NP ⊆ RTIME(2poly(log n)), we show that there is no polynomialtime (log n) ..."
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Cited by 62 (2 self)
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Abstract. Let p> 1beany fixed real. We show that assuming NP ⊆ RP, there is no polynomial time algorithm that approximates the Shortest Vector Problem (SVP) in ℓp norm within a constant factor. Under the stronger assumption NP ⊆ RTIME(2poly(log n)), we show that there is no polynomialtime (log n)1/2−ɛ algorithm with approximation ratio 2 where n is the dimension of the lattice and ɛ>0isan arbitrarily small constant. We first give a new (randomized) reduction from Closest Vector Problem (CVP) to SVP that achieves some constant factor hardness. The reduction is based on BCH Codes. Its advantage is that the SVP instances produced by the reduction behave well under the augmented tensor product,anew (log n)1/2−ɛ variant of tensor product that we introduce. This enables us to boost the hardness factor to 2.
Are bitvectors optimal?
"... ... We show lower bounds that come close to our upper bounds (for a large range of n and ffl): Schemes that answer queries with just one bitprobe and error probability ffl must use \Omega ( nffl log(1=ffl) log m) bits of storage; if the error is restricted to queries not in S, then the scheme must u ..."
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Cited by 57 (7 self)
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... We show lower bounds that come close to our upper bounds (for a large range of n and ffl): Schemes that answer queries with just one bitprobe and error probability ffl must use \Omega ( nffl log(1=ffl) log m) bits of storage; if the error is restricted to queries not in S, then the scheme must use \Omega ( n2ffl2 log(n=ffl) log m) bits of storage. We also
On the Fourier Spectrum of Monotone Functions
, 1996
"... In this paper, monotone Boolean functions are studied using harmonic analysis on the cube. ..."
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Cited by 48 (1 self)
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In this paper, monotone Boolean functions are studied using harmonic analysis on the cube.
The two possible values of the chromatic number of a random graph
 Ann. Math
"... Given d ∈ (0, ∞) let kd be the smallest integer k such that d < 2k log k. We prove that the chromatic number of a random graph G(n,d/n) is either kd or kd + 1 almost surely. 1. ..."
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Cited by 47 (6 self)
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Given d ∈ (0, ∞) let kd be the smallest integer k such that d < 2k log k. We prove that the chromatic number of a random graph G(n,d/n) is either kd or kd + 1 almost surely. 1.
Testing Juntas
, 2002
"... We show that a Boolean function over n Boolean variables can be tested for the property of depending on only k of them, using a number of queries that depends only on k and the approximation parameter . We present two tests, both nonadaptive, that require a number of queries that is polynomial k an ..."
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Cited by 46 (8 self)
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We show that a Boolean function over n Boolean variables can be tested for the property of depending on only k of them, using a number of queries that depends only on k and the approximation parameter . We present two tests, both nonadaptive, that require a number of queries that is polynomial k and linear in . The first test is stronger in that it has a 1sided error, while the second test has a more compact analysis. We also present an adaptive version and a 2sided error version of the first test, that have a somewhat better query complexity than the other algorithms...
Quantum Fingerprinting
, 2001
"... Classical ngerprinting associates with each string a shorter string (its ngerprint) , such that, with high probability, any two distinct strings can be distinguished by comparing their ngerprints alone. The ngerprints can be exponentially smaller than the original strings if the parties preparing ..."
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Cited by 44 (13 self)
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Classical ngerprinting associates with each string a shorter string (its ngerprint) , such that, with high probability, any two distinct strings can be distinguished by comparing their ngerprints alone. The ngerprints can be exponentially smaller than the original strings if the parties preparing the ngerprints share a random key, but not if they only have access to uncorrelated random sources. In this paper we show that ngerprints consisting of quantum information can be made exponentially smaller than the original strings without any correlations or entanglement between the parties. In our scheme, the ngerprints are exponentially shorter than the original strings and a measurement distinguishes between the ngerprints of any two distinct strings. Our scheme implies an exponential quantum/classical gap for the equality problem in the simultaneous message passing model of communication complexity. We optimize several aspects of our scheme. Typeset using REVT E X 1...