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Factoring wavelet transforms into lifting steps
 J. FOURIER ANAL. APPL
, 1998
"... This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decompositio ..."
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Cited by 584 (8 self)
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present here a selfcontained derivation, building the decomposition from basic principles such as the Euclidean algorithm, with a focus on applying it to wavelet filtering. This factorization provides an alternative for the lattice factorization, with the advantage that it can also be used
Implementing data cubes efficiently
 In SIGMOD
, 1996
"... Decision support applications involve complex queries on very large databases. Since response times should be small, query optimization is critical. Users typically view the data as multidimensional data cubes. Each cell of the data cube is a view consisting of an aggregation of interest, like total ..."
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Cited by 548 (1 self)
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to materialize. The greedy algorithm performs within a small constant factor of optimal under a variety of models. We then consider the most common case of the hypercube lattice and examine the choice of materialized views for hypercubes in detail, giving some good tradeoffs between the space used
Capacity of Ad Hoc Wireless Networks
"... Early simulation experience with wireless ad hoc networks suggests that their capacity can be surprisingly low, due to the requirement that nodes forward each others’ packets. The achievable capacity depends on network size, traffic patterns, and detailed local radio interactions. This paper examine ..."
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Cited by 636 (14 self)
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examines these factors alone and in combination, using simulation and analysis from first principles. Our results include both specific constants and general scaling relationships helpful in understanding the limitations of wireless ad hoc networks. We examine interactions of the 802.11 MAC and ad hoc
On Lattices, Learning with Errors, Random Linear Codes, and Cryptography
 In STOC
, 2005
"... Our main result is a reduction from worstcase lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the ‘learning from parity with error’ problem to higher moduli. It can also be viewed as the problem of decoding from a random linear co ..."
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Cited by 364 (6 self)
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Our main result is a reduction from worstcase lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the ‘learning from parity with error’ problem to higher moduli. It can also be viewed as the problem of decoding from a random linear
SPADE: An efficient algorithm for mining frequent sequences
 Machine Learning
, 2001
"... Abstract. In this paper we present SPADE, a new algorithm for fast discovery of Sequential Patterns. The existing solutions to this problem make repeated database scans, and use complex hash structures which have poor locality. SPADE utilizes combinatorial properties to decompose the original proble ..."
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Cited by 437 (16 self)
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problem into smaller subproblems, that can be independently solved in mainmemory using efficient lattice search techniques, and using simple join operations. All sequences are discovered in only three database scans. Experiments show that SPADE outperforms the best previous algorithm by a factor of two
On the Completeness of the Lattice Factorization for LinearPhase Perfect Reconstruction Filter Banks
"... Abstract—In this letter, we reexamine the completeness of the lattice factorization forchannel linearphase perfect reconstruction filter bank (LPPRFB) with filters of the same length = in [1]. We point out that the assertion of completeness in [1] is incorrect. Examples are presented to show that ..."
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Abstract—In this letter, we reexamine the completeness of the lattice factorization forchannel linearphase perfect reconstruction filter bank (LPPRFB) with filters of the same length = in [1]. We point out that the assertion of completeness in [1] is incorrect. Examples are presented to show
MAFIA: A maximal frequent itemset algorithm for transactional databases
 In ICDE
, 2001
"... We present a new algorithm for mining maximal frequent itemsets from a transactional database. Our algorithm is especially efficient when the itemsets in the database are very long. The search strategy of our algorithm integrates a depthfirst traversal of the itemset lattice with effective pruning ..."
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Cited by 309 (3 self)
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We present a new algorithm for mining maximal frequent itemsets from a transactional database. Our algorithm is especially efficient when the itemsets in the database are very long. The search strategy of our algorithm integrates a depthfirst traversal of the itemset lattice with effective pruning
LATTICE FACTORIZATION AND DESIGN OF PERFECT RECONSTRUCTION FILTER BANKS WITH ANY LENGTH YIELDING LINEAR PHASE
"... This paper introduces the lattice factorizations and designs of a large class of critically sampled linear phase perfect reconstruction lter banks. We deal with FIR lter banks with realvalued coefcients in which all lters have the same arbitrary length and symmetry center. Rened existence condition ..."
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This paper introduces the lattice factorizations and designs of a large class of critically sampled linear phase perfect reconstruction lter banks. We deal with FIR lter banks with realvalued coefcients in which all lters have the same arbitrary length and symmetry center. Rened existence
Trapdoors for Hard Lattices and New Cryptographic Constructions
, 2007
"... We show how to construct a variety of “trapdoor ” cryptographic tools assuming the worstcase hardness of standard lattice problems (such as approximating the shortest nonzero vector to within small factors). The applications include trapdoor functions with preimage sampling, simple and efficient “ha ..."
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Cited by 191 (26 self)
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We show how to construct a variety of “trapdoor ” cryptographic tools assuming the worstcase hardness of standard lattice problems (such as approximating the shortest nonzero vector to within small factors). The applications include trapdoor functions with preimage sampling, simple and efficient
The Hardness of Approximate Optima in Lattices, Codes, and Systems of Linear Equations
, 1993
"... We prove the following about the Nearest Lattice Vector Problem (in any `p norm), the Nearest Codeword Problem for binary codes, the problem of learning a halfspace in the presence of errors, and some other problems. 1. Approximating the optimum within any constant factor is NPhard. 2. If for some ..."
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Cited by 170 (7 self)
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We prove the following about the Nearest Lattice Vector Problem (in any `p norm), the Nearest Codeword Problem for binary codes, the problem of learning a halfspace in the presence of errors, and some other problems. 1. Approximating the optimum within any constant factor is NPhard. 2
Results 1  10
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