Results 1  10
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303
Multiparty Communication Complexity
, 1989
"... A given Boolean function has its input distributed among many parties. The aim is to determine which parties to tMk to and what information to exchange with each of them in order to evaluate the function while minimizing the total communication. This paper shows that it is possible to obtain the Boo ..."
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Cited by 760 (22 self)
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A given Boolean function has its input distributed among many parties. The aim is to determine which parties to tMk to and what information to exchange with each of them in order to evaluate the function while minimizing the total communication. This paper shows that it is possible to obtain the Boolean answer deterministically with only a polynomial increase in communication with respect to the information lower bound given by the nondeterministic communication complexity of the function.
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 475 (67 self)
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We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being kcolorable or having a aeclique (clique of density ae w.r.t the vertex set). Our graph property testing algorithms are probabilistic and make assertions which are correct with high probability, utilizing only poly(1=ffl) edgequeries into the graph, where ffl is the distance parameter. Moreover, the property testing algorithms can be used to efficiently (i.e., in time linear in the number of vertices) construct partitions of the graph which corre...
Probabilistic checking of proofs: a new characterization of NP
 JOURNAL OF THE ACM
, 1998
"... We give a new characterization of NP: the class NP contains exactly those languages L for which membership proofs (a proof that an input x is in L) can be verified probabilistically in polynomial time using logarithmic number of random bits and by reading sublogarithmic number of bits from the proof ..."
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Cited by 414 (26 self)
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We give a new characterization of NP: the class NP contains exactly those languages L for which membership proofs (a proof that an input x is in L) can be verified probabilistically in polynomial time using logarithmic number of random bits and by reading sublogarithmic number of bits from the proof. We discuss implications of this characterization; specifically, we show that approximating Clique and Independent Set, even in a very weak sense, is NPhard.
Visual Cryptography
 A PRELIMINARY VERSION OF THIS PAPER APPEARED IN EUROCRYPT 94.
"... In this paper we consider a new type of cryptographic scheme, which can decode concealed images without any cryptographic computations. The scheme is perfectly secure and very easy to implement. We extend it into a visual variant ofthek out of n secret sharing problem, in which a dealer provides a t ..."
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Cited by 327 (4 self)
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In this paper we consider a new type of cryptographic scheme, which can decode concealed images without any cryptographic computations. The scheme is perfectly secure and very easy to implement. We extend it into a visual variant ofthek out of n secret sharing problem, in which a dealer provides a transparency to each one of the n users � any k of them can see the image by stacking their transparencies, but any k  1 of them gain no information about it.
SmallBias Probability Spaces: Efficient Constructions and Applications
 SIAM J. Comput
, 1993
"... We show how to efficiently construct a small probability space on n binary random variables such that for every subset, its parity is either zero or one with "almost" equal probability. They are called fflbiased random variables. The number of random bits needed to generate the random var ..."
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Cited by 276 (13 self)
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We show how to efficiently construct a small probability space on n binary random variables such that for every subset, its parity is either zero or one with "almost" equal probability. They are called fflbiased random variables. The number of random bits needed to generate the random variables is O(log n + log 1 ffl ). Thus, if ffl is polynomially small, then the size of the sample space is also polynomial. Random variables that are fflbiased can be used to construct "almost" kwise independent random variables where ffl is a function of k. These probability spaces have various applications: 1. Derandomization of algorithms: many randomized algorithms that require only k wise independence of their random bits (where k is bounded by O(log n)), can be derandomized by using fflbiased random variables. 2. Reducing the number of random bits required by certain randomized algorithms, e.g., verification of matrix multiplication. 3. Exhaustive testing of combinatorial circui...
Minwise Independent Permutations
 Journal of Computer and System Sciences
, 1998
"... We define and study the notion of minwise independent families of permutations. We say that F ⊆ Sn is minwise independent if for any set X ⊆ [n] and any x ∈ X, when π is chosen at random in F we have Pr(min{π(X)} = π(x)) = 1 X . In other words we require that all the elements of any fixed set ..."
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Cited by 276 (11 self)
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We define and study the notion of minwise independent families of permutations. We say that F ⊆ Sn is minwise independent if for any set X ⊆ [n] and any x ∈ X, when π is chosen at random in F we have Pr(min{π(X)} = π(x)) = 1 X . In other words we require that all the elements of any fixed set X have an equal chance to become the minimum element of the image of X under π. Our research was motivated by the fact that such a family (under some relaxations) is essential to the algorithm used in practice by the AltaVista web index software to detect and filter nearduplicate documents. However, in the course of our investigation we have discovered interesting and challenging theoretical questions related to this concept – we present the solutions to some of them and we list the rest as open problems.
Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals
, 2009
"... Wideband analog signals push contemporary analogtodigital conversion systems to their performance limits. In many applications, however, sampling at the Nyquist rate is inefficient because the signals of interest contain only a small number of significant frequencies relative to the bandlimit, alt ..."
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Cited by 158 (18 self)
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Wideband analog signals push contemporary analogtodigital conversion systems to their performance limits. In many applications, however, sampling at the Nyquist rate is inefficient because the signals of interest contain only a small number of significant frequencies relative to the bandlimit, although the locations of the frequencies may not be known a priori. For this type of sparse signal, other sampling strategies are possible. This paper describes a new type of data acquisition system, called a random demodulator, that is constructed from robust, readily available components. Let K denote the total number of frequencies in the signal, and let W denote its bandlimit in Hz. Simulations suggest that the random demodulator requires just O(K log(W/K)) samples per second to stably reconstruct the signal. This sampling rate is exponentially lower than the Nyquist rate of W Hz. In contrast with Nyquist sampling, one must use nonlinear methods, such as convex programming, to recover the signal from the samples taken by the random demodulator. This paper provides a detailed theoretical analysis of the system’s performance that supports the empirical observations.
From theory to practice: SubNyquist sampling of sparse wideband analog signals
 IEEE J. SEL. TOPICS SIGNAL PROCESS
, 2010
"... Conventional subNyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind subNyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. ..."
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Cited by 153 (55 self)
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Conventional subNyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind subNyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then lowpass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, realtime performance for signals with timevarying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of stateoftheart analog conversion technologies such as interleaved converters.
Entropy waves, the zigzag graph product, and new constantdegree expanders
, 2002
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ChernoffHoeffding bounds for applications with limited independence.
 In Proceedings of the 4th Annual ACMSIAM Symposium on Discrete Algorithms,
, 1993
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