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13,857
An algorithm for modular exponentiation
 Information Processing Letters
, 1998
"... A practical technique for improving the performance of modular exponentiations (ME) is described. The complexity of the ME algorithm is O modular multiplications (MMs), where n is the length of the exponent, requiring an O ( n 2) precomputed lookup table size with very small constant of proportiona ..."
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Cited by 31 (9 self)
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A practical technique for improving the performance of modular exponentiations (ME) is described. The complexity of the ME algorithm is O modular multiplications (MMs), where n is the length of the exponent, requiring an O ( n 2) precomputed lookup table size with very small constant
An Algorithm for Modular Exponentiation
"... A practical technique for improving the performance of modular exponentiations (ME) is described. The complexity of the ME algorithm is O n ⎛⎝logn⎠ modular multiplications (MMs), where n is the length of the exponent, requiring an O(n 2) precomputed lookup table size with very small const ..."
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A practical technique for improving the performance of modular exponentiations (ME) is described. The complexity of the ME algorithm is O n ⎛⎝logn⎠ modular multiplications (MMs), where n is the length of the exponent, requiring an O(n 2) precomputed lookup table size with very small
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 819 (28 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
Graphbased algorithms for Boolean function manipulation
 IEEE TRANSACTIONS ON COMPUTERS
, 1986
"... In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on th ..."
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Cited by 3526 (46 self)
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on the ordering of decision variables in the graph. Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. Our algorithms have time complexity proportional
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 522 (15 self)
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case exponenti al ti me complexi ty. However, we show that for manysiB7 ti ns i whi h ...
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 502 (0 self)
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We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible
Depthfirst IterativeDeepening: An Optimal Admissible Tree Search
 Artificial Intelligence
, 1985
"... The complexities of various search algorithms are considered in terms of time, space, and cost of solution path. It is known that breadthfirst search requires too much space and depthfirst search can use too much time and doesn't always find a cheapest path. A depthfirst iteratiwdeepening a ..."
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Cited by 527 (24 self)
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deepening algorithm is shown to be asymptotically optimal along all three dimensions for exponential pee searches. The algorithm has been used successfully in chess programs, has been eflectiuely combined with bidirectional search, and has been applied to bestfirst heuristic search as well. This heuristic depth
A simple distributed autonomous power control algorithm and its convergence
 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY
, 1993
"... For wireless cellular communication systems, one seeks a simple effective means of power control of signals associated with randomly dispersed users that are reusing a single channel in different cells. By effecting the lowest interference environment, in meeting a required minimum signaltointerf ..."
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Cited by 477 (3 self)
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distributed type of algorithm, whenever power settings exist for which all users meet the p requirement, we demonstrate exponentially fast convergence to these settings.
MACAW: A Media Access Protocol for Wireless LAN's
"... In recent years, a wide variety of mobile computing devices has emerged, including portables, palmtops, and personal digital assistants. Providing adequate network connectivity for these devices will require a new generation of wireless LAN technology. In this paper we study media access protocols f ..."
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Cited by 839 (11 self)
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for a single channel wireless LAN being developed at Xerox Corporation's Palo Alto Research Center. We start with the MACA media access protocol rst proposed by Karn [9] and later refined by Biba [3] which uses an RTSCTSDATA packet exchange and binary exponential backo. Using packet
Large margin methods for structured and interdependent output variables
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2005
"... Learning general functional dependencies between arbitrary input and output spaces is one of the key challenges in computational intelligence. While recent progress in machine learning has mainly focused on designing flexible and powerful input representations, this paper addresses the complementary ..."
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Cited by 624 (12 self)
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to accomplish this, we propose to appropriately generalize the wellknown notion of a separation margin and derive a corresponding maximummargin formulation. While this leads to a quadratic program with a potentially prohibitive, i.e. exponential, number of constraints, we present a cutting plane algorithm
Results 1  10
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