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ABSTRACT A 3Query PCP over Integers
"... A classic result due to H˚astad [11] established that for every constant ε> 0, given an overdetermined system of linear equations over a finite field Fq where each equation depends on exactly 3 variables and at least a fraction (1 − ε) of the equations “ can be ” satisfied, it is NPhard to satis ..."
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hard to satisfy even a 1 fraction + ε of the equations. q In this work, we prove the analog of H˚astad’s result for equations over the integers (as well as the reals). Formally, we prove that for every ε, δ> 0, given a system of linear equations with integer coefficients where each equation is on 3 variables
HARDNESS OF SOLVING SPARSE OVERDETERMINED LINEAR SYSTEMS: A 3QUERY PCP OVER INTEGERS
"... Abstract. A classic result due to H˚astad established that for every constant ε> 0, given an overdetermined system of linear equations over a finite field Fq where each equation depends on exactly 3 variables and at least a fraction (1 − ε) of the equations can be satisfied, it is NPhard to sati ..."
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Cited by 1 (0 self)
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hard to satisfy even a fraction ` 1 q + ε ´ of the equations. In this work, we prove the analog of H˚astad’s result for equations over the integers (as well as the reals). Formally, we prove that for every ε, δ> 0, given a system of linear equations with integer coefficients where each equation is on 3
The Encyclopedia of Integer Sequences
"... This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs ..."
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Cited by 866 (15 self)
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This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae
The Omega Test: a fast and practical integer programming algorithm for dependence analysis
 Communications of the ACM
, 1992
"... The Omega testi s ani nteger programmi ng algori thm that can determi ne whether a dependence exi sts between two array references, and i so, under what condi7: ns. Conventi nalwi[A m holds thati nteger programmiB techni:36 are far too expensi e to be used for dependence analysi6 except as a method ..."
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Cited by 521 (15 self)
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The Omega testi s ani nteger programmi ng algori thm that can determi ne whether a dependence exi sts between two array references, and i so, under what condi7: ns. Conventi nalwi[A m holds thati nteger programmiB techni:36 are far too expensi e to be used for dependence analysi6 except as a method
Tinydb: An acquisitional query processing system for sensor networks
 ACM Trans. Database Syst
, 2005
"... We discuss the design of an acquisitional query processor for data collection in sensor networks. Acquisitional issues are those that pertain to where, when, and how often data is physically acquired (sampled) and delivered to query processing operators. By focusing on the locations and costs of acq ..."
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Cited by 609 (8 self)
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of acquiring data, we are able to significantly reduce power consumption over traditional passive systems that assume the a priori existence of data. We discuss simple extensions to SQL for controlling data acquisition, and show how acquisitional issues influence query optimization, dissemination
Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations
, 2005
"... How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include hea ..."
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Cited by 534 (48 self)
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How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include
Querying Heterogeneous Information Sources Using Source Descriptions
, 1996
"... We witness a rapid increase in the number of structured information sources that are available online, especially on the WWW. These sources include commercial databases on product information, stock market information, real estate, automobiles, and entertainment. We would like to use the data stored ..."
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Cited by 727 (35 self)
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featured database systems and can answer only a small set of queries over their data (for example, forms on the WWW restrict the set of queries one can ask). (3) Since the number of sources is very large, effective techniques are needed to prune the set of information sources accessed to answer a query. (4
Fast subsequence matching in timeseries databases
 PROCEEDINGS OF THE 1994 ACM SIGMOD INTERNATIONAL CONFERENCE ON MANAGEMENT OF DATA
, 1994
"... We present an efficient indexing method to locate 1dimensional subsequences within a collection of sequences, such that the subsequences match a given (query) pattern within a specified tolerance. The idea is to map each data sequence into a small set of multidimensional rectangles in feature space ..."
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Cited by 528 (24 self)
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We present an efficient indexing method to locate 1dimensional subsequences within a collection of sequences, such that the subsequences match a given (query) pattern within a specified tolerance. The idea is to map each data sequence into a small set of multidimensional rectangles in feature
A Digital Signature Scheme Secure Against Adaptive ChosenMessage Attacks
, 1995
"... We present a digital signature scheme based on the computational diculty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosenmessage attack: an adversary who receives signatures for messages of his choice (where each message may be chosen in a ..."
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Cited by 985 (43 self)
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We present a digital signature scheme based on the computational diculty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosenmessage attack: an adversary who receives signatures for messages of his choice (where each message may be chosen
Modular elliptic curves and Fermat’s Last Theorem
 ANNALS OF MATH
, 1995
"... When Andrew John Wiles was 10 years old, he read Eric Temple Bell’s The Last Problem and was so impressed by it that he decided that he would be the first person to prove Fermat’s Last Theorem. This theorem states that there are no nonzero integers a, b, c, n with n> 2 such that a n + b n = c n ..."
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Cited by 612 (1 self)
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When Andrew John Wiles was 10 years old, he read Eric Temple Bell’s The Last Problem and was so impressed by it that he decided that he would be the first person to prove Fermat’s Last Theorem. This theorem states that there are no nonzero integers a, b, c, n with n> 2 such that a n + b n = c
Results 1  10
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