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Fast Modular Exponentiation
"... The wellknown binary method computes C = M E #mod N# using an average number of 1:5#n , 1# multiplications, where n is the number of bits in the binary expansion of E. When the exponent is recoded using the canonical bit recoding technique then the average number of multiplications can be reduc ..."
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The wellknown binary method computes C = M E #mod N# using an average number of 1:5#n , 1# multiplications, where n is the number of bits in the binary expansion of E. When the exponent is recoded using the canonical bit recoding technique then the average number of multiplications can be reduced to 1:33#n , 1#. We show that a further reduction is achieved if the bits of the exponent are scanned at d#1 bits at a time: for n =2 10 , for example, the average number of multiplications becomes 1:212#n , 1# with d =5.Furthermore, given any ##0, the computation can be done using an average of #1 + ###n , 1# multiplications for large n by taking d = d 1 # e.
New Modular Multiplication Algorithms for Fast Modular Exponentiation
 in “Advances in Cryptology—Proceedings of Eurocrypt ’96
, 1996
"... . A modular exponentiation is one of the most important operations in publickey cryptography. However, it takes much time because the modular exponentiation deals with very large operands as 512bit integers. The modular exponentiation is composed of repetition of modular multiplications. Therefore ..."
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Cited by 11 (0 self)
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. A modular exponentiation is one of the most important operations in publickey cryptography. However, it takes much time because the modular exponentiation deals with very large operands as 512bit integers. The modular exponentiation is composed of repetition of modular multiplications
The click modular router
, 2001
"... Click is a new software architecture for building flexible and configurable routers. A Click router is assembled from packet processing modules called elements. Individual elements implement simple router functions like packet classification, queueing, scheduling, and interfacing with network devic ..."
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Cited by 1155 (28 self)
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language tools that optimize router configurations and ensure they satisfy simple invariants. Due to Click’s architecture and language, Click router configurations are modular and easy to extend. A standardscompliant Click IP router has sixteen elements on its forwarding path. We present extensions
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing
Fast Algorithms for Mining Association Rules
, 1994
"... We consider the problem of discovering association rules between items in a large database of sales transactions. We present two new algorithms for solving this problem that are fundamentally different from the known algorithms. Empirical evaluation shows that these algorithms outperform the known a ..."
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Cited by 3551 (15 self)
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We consider the problem of discovering association rules between items in a large database of sales transactions. We present two new algorithms for solving this problem that are fundamentally different from the known algorithms. Empirical evaluation shows that these algorithms outperform the known algorithms by factors ranging from three for small problems to more than an order of magnitude for large problems. We also show how the best features of the two proposed algorithms can be combined into a hybrid algorithm, called AprioriHybrid. Scaleup experiments show that AprioriHybrid scales linearly with the number of transactions. AprioriHybrid also has excellent scaleup properties with respect to the transaction size and the number of items in the database.
Fast Planning Through Planning Graph Analysis
 ARTIFICIAL INTELLIGENCE
, 1995
"... We introduce a new approach to planning in STRIPSlike domains based on constructing and analyzing a compact structure we call a Planning Graph. We describe a new planner, Graphplan, that uses this paradigm. Graphplan always returns a shortest possible partialorder plan, or states that no valid pla ..."
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Cited by 1165 (3 self)
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We introduce a new approach to planning in STRIPSlike domains based on constructing and analyzing a compact structure we call a Planning Graph. We describe a new planner, Graphplan, that uses this paradigm. Graphplan always returns a shortest possible partialorder plan, or states that no valid plan exists. We provide empirical evidence in favor of this approach, showing that Graphplan outperforms the totalorder planner, Prodigy, and the partialorder planner, UCPOP, on a variety of interesting natural and artificial planning problems. We also give empirical evidence that the plans produced by Graphplan are quite sensible. Since searches made by this approach are fundamentally different from the searches of other common planning methods, they provide a new perspective on the planning problem.
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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case exponenti al ti me complexi ty. However, we show that for manysiB7 ti ns i whi h ...
A Simple, Fast, and Accurate Algorithm to Estimate Large Phylogenies by Maximum Likelihood
, 2003
"... The increase in the number of large data sets and the complexity of current probabilistic sequence evolution models necessitates fast and reliable phylogeny reconstruction methods. We describe a new approach, based on the maximumlikelihood principle, which clearly satisfies these requirements. The ..."
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Cited by 2109 (30 self)
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The increase in the number of large data sets and the complexity of current probabilistic sequence evolution models necessitates fast and reliable phylogeny reconstruction methods. We describe a new approach, based on the maximumlikelihood principle, which clearly satisfies these requirements
FAST VOLUME RENDERING USING A SHEARWARP FACTORIZATION OF THE VIEWING TRANSFORMATION
, 1995
"... Volume rendering is a technique for visualizing 3D arrays of sampled data. It has applications in areas such as medical imaging and scientific visualization, but its use has been limited by its high computational expense. Early implementations of volume rendering used bruteforce techniques that req ..."
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Cited by 541 (2 self)
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that require on the order of 100 seconds to render typical data sets on a workstation. Algorithms with optimizations that exploit coherence in the data have reduced rendering times to the range of ten seconds but are still not fast enough for interactive visualization applications. In this thesis we present a
A Fast and Elitist MultiObjective Genetic Algorithm: NSGAII
, 2000
"... Multiobjective evolutionary algorithms which use nondominated sorting and sharing have been mainly criticized for their (i) O(MN computational complexity (where M is the number of objectives and N is the population size), (ii) nonelitism approach, and (iii) the need for specifying a sharing param ..."
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Cited by 1707 (58 self)
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parameter. In this paper, we suggest a nondominated sorting based multiobjective evolutionary algorithm (we called it the Nondominated Sorting GAII or NSGAII) which alleviates all the above three difficulties. Specifically, a fast nondominated sorting approach with O(MN ) computational complexity
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