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187
SPIRAL: Code Generation for DSP Transforms
 PROCEEDINGS OF THE IEEE SPECIAL ISSUE ON PROGRAM GENERATION, OPTIMIZATION, AND ADAPTATION
, 2005
"... Abstract — Fast changing, increasingly complex, and diverse computing platforms pose central problems in scientific computing: How to achieve, with reasonable effort, portable optimal performance? We present SPIRAL that considers this problem for the performancecritical domain of linear digital sig ..."
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Cited by 141 (31 self)
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Abstract — Fast changing, increasingly complex, and diverse computing platforms pose central problems in scientific computing: How to achieve, with reasonable effort, portable optimal performance? We present SPIRAL that considers this problem for the performancecritical domain of linear digital signal processing (DSP) transforms. For a specified transform, SPIRAL automatically generates high performance code that is tuned to the given platform. SPIRAL formulates the tuning as an optimization problem, and exploits the domainspecific mathematical structure of transform algorithms to implement a feedbackdriven optimizer. Similar to a human expert, for a specified transform, SPIRAL “intelligently ” generates and explores algorithmic and implementation choices to find the best match to the computer’s microarchitecture. The “intelligence” is provided by search and learning techniques that exploit the structure of the algorithm and implementation space to guide the exploration and optimization. SPIRAL generates high performance code for a broad set of DSP transforms including the discrete Fourier transform, other trigonometric transforms, filter transforms, and discrete wavelet transforms. Experimental results show that the code generated by SPIRAL competes with, and sometimes outperforms, the best available human tuned transform library code. Index Terms — library generation, code optimization, adaptation, automatic performance tuning, high performance computing, linear signal transform, discrete Fourier transform, FFT, discrete cosine transform, wavelet, filter, search, learning, genetic and evolutionary algorithm, Markov decision process I.
On the NesterovTodd direction in semidefinite programming
 SIAM Journal on Optimization
, 1996
"... Nesterov and Todd discuss several pathfollowing and potentialreduction interiorpoint methods for certain convex programming problems. In the special case of semidefinite programming, we discuss how to compute the corresponding directions efficiently, how to view them as Newton directions, and how ..."
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Cited by 108 (22 self)
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Nesterov and Todd discuss several pathfollowing and potentialreduction interiorpoint methods for certain convex programming problems. In the special case of semidefinite programming, we discuss how to compute the corresponding directions efficiently, how to view them as Newton directions, and how to take Mehrotra predictorcorrector steps in this framework. We also provide some computational results suggesting that our algorithm is more robust than alternative methods.
Fundamental Bounds and Approximations for ATM Multiplexers with Applications to Video Teleconferencing
, 1995
"... The main contributions of this paper are twofold. First, we prove fundamental, similarly behaving lower and upper bounds, and give an approximation based on the bounds, which is effective for analyzing ATM multiplexers, even when the traffic has many, possibly heterogeneous, sources and their model ..."
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Cited by 105 (12 self)
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The main contributions of this paper are twofold. First, we prove fundamental, similarly behaving lower and upper bounds, and give an approximation based on the bounds, which is effective for analyzing ATM multiplexers, even when the traffic has many, possibly heterogeneous, sources and their models are of high dimension. Second, we apply our analytic approximation to statistical models of video teleconference traffic, obtain the multiplexing system's capacity as determined by the number of admissible sources for given cell loss probability, buffer size and trunk bandwidth, and, finally, compare with results from simulations, which are driven by actual data from coders. The results are surprisingly close. Our bounds are based on Large Deviations theory. The main assumption is that the sources are Markovian and timereversible. Our approximation to the steady state buffer distribution is called "ChernoffDominant Eigenvalue" since one parameter is obtained from Chernoff's theorem and t...
The Quadratic Assignment Problem: A Survey and Recent Developments
 In Proceedings of the DIMACS Workshop on Quadratic Assignment Problems, volume 16 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1994
"... . Quadratic Assignment Problems model many applications in diverse areas such as operations research, parallel and distributed computing, and combinatorial data analysis. In this paper we survey some of the most important techniques, applications, and methods regarding the quadratic assignment probl ..."
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Cited by 91 (16 self)
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. Quadratic Assignment Problems model many applications in diverse areas such as operations research, parallel and distributed computing, and combinatorial data analysis. In this paper we survey some of the most important techniques, applications, and methods regarding the quadratic assignment problem. We focus our attention on recent developments. 1. Introduction Given a set N = f1; 2; : : : ; ng and n \Theta n matrices F = (f ij ) and D = (d kl ), the quadratic assignment problem (QAP) can be stated as follows: min p2\Pi N n X i=1 n X j=1 f ij d p(i)p(j) + n X i=1 c ip(i) ; where \Pi N is the set of all permutations of N . One of the major applications of the QAP is in location theory where the matrix F = (f ij ) is the flow matrix, i.e. f ij is the flow of materials from facility i to facility j, and D = (d kl ) is the distance matrix, i.e. d kl represents the distance from location k to location l [62, 67, 137]. The cost of simultaneously assigning facility i to locat...
Edge Detection with Embedded Confidence
 IEEE Trans. Pattern Anal. Machine Intell
, 2001
"... Computing the weighted average of the pixel values in a window is a basic module in many computer vision operators. The process is reformulated in a linear vector space and the role of the different subspaces is emphasized. Within this framework well known artifacts of the gradient based edge dete ..."
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Cited by 70 (1 self)
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Computing the weighted average of the pixel values in a window is a basic module in many computer vision operators. The process is reformulated in a linear vector space and the role of the different subspaces is emphasized. Within this framework well known artifacts of the gradient based edge detectors, such as large spurious responses can be explained quantitatively. It is also shown that template matching with a template derived from the input data is meaningful since it provides an independent measure of confidence in the presence of the employed edge model. The widely used threestep edge detection procedure: gradient estimation, nonmaxima suppression, hysteresis thresholding; is generalized to include the information provided by the confidence measure. The additional amount of computation is minimal and experiments with several standard test images show the ability of the new procedure to detect weak edges. Keywords: edge detection, performance assessment, gradient estimation, window operators 1
A Decentralized Approach to Formation Maneuvers
 IEEE Transactions on Robotics and Automation
, 2003
"... Abstract—This paper presents a behaviorbased approach to formation maneuvers for groups of mobile robots. Complex formation maneuvers are decomposed into a sequence of maneuvers between formation patterns. The paper presents three formation control strategies. The first strategy uses relative posit ..."
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Cited by 63 (0 self)
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Abstract—This paper presents a behaviorbased approach to formation maneuvers for groups of mobile robots. Complex formation maneuvers are decomposed into a sequence of maneuvers between formation patterns. The paper presents three formation control strategies. The first strategy uses relative position information configured in a bidirectional ring topology to maintain the formation. The second strategy injects interrobot damping via passivity techniques. The third strategy accounts for actuator saturation. Hardware results demonstrate the effectiveness of the proposed control strategies. Index Terms—Behavioral methods, coordinated control, formations, mobile robots, passivity.
Classes of kernels for machine learning: a statistics perspective
 Journal of Machine Learning Research
, 2001
"... In this paper, we present classes of kernels for machine learning from a statistics perspective. Indeed, kernels are positive definite functions and thus also covariances. After discussing key properties of kernels, as well as a new formula to construct kernels, we present several important classes ..."
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Cited by 59 (2 self)
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In this paper, we present classes of kernels for machine learning from a statistics perspective. Indeed, kernels are positive definite functions and thus also covariances. After discussing key properties of kernels, as well as a new formula to construct kernels, we present several important classes of kernels: anisotropic stationary kernels, isotropic stationary kernels, compactly supportedkernels, locally stationary kernels, nonstationary kernels, andseparable nonstationary kernels. Compactly supportedkernels andseparable nonstationary kernels are of prime interest because they provide a computational reduction for kernelbased methods. We describe the spectral representation of the various classes of kernels and conclude with a discussion on the characterization of nonlinear maps that reduce nonstationary kernels to either stationarity or local stationarity.
Controlling Connectivity of Dynamic Graphs
, 2005
"... The control of mobile networks of multiple agents raises fundamental and novel problems in controlling the structure of the resulting dynamic graphs. In this paper, we consider the problem of controlling a network of agents so that the resulting motion always preserves various connectivity propertie ..."
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Cited by 46 (5 self)
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The control of mobile networks of multiple agents raises fundamental and novel problems in controlling the structure of the resulting dynamic graphs. In this paper, we consider the problem of controlling a network of agents so that the resulting motion always preserves various connectivity properties. In particular, we consider preserving khop connectivity, where agents are allowed to move while maintaining connections to agents that are no more than khops away. The connectivity constraint is translated to constrains on individual agent motion by considering the dynamics of the adjacency matrix and related constructs from algebraic graph theory. As special cases, we obtain motion constraints that can preserve the exact structure of the initial dynamic graph, or may simply preserve the usual notion connectivity while the structure of the graph changes over time. We conclude by illustrating various interesting problems that can be achieved while preserving connectivity constraints.
Surface Fitting with Hierarchical Splines
 ACM Transactions on Graphics
, 1995
"... We consider the fitting of tensor product parametric spline surfaces to gridded data. The continuity of the surface is provided by the basis chosen. When tensor product splines are used with gridded data, the surface fitting problem decomposes into a sequence of curve fitting processes, making the c ..."
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Cited by 44 (1 self)
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We consider the fitting of tensor product parametric spline surfaces to gridded data. The continuity of the surface is provided by the basis chosen. When tensor product splines are used with gridded data, the surface fitting problem decomposes into a sequence of curve fitting processes, making the computations particularly e#cient. The use of a hierarchical representation for the surface adds further e#ciency by adaptively decomposing the fitting process into subproblems involving only a portion of the data. Hierarchy also provides a means of storing the resulting surface in a compressed format. Our approach is compared to multiresolution analysis and the use of wavelets. 1 Introduction In [9] an adaptive process was presented for fitting surface data with a geometrically continuous collection of rectangular Bezier patches. The adaptivity resulted from fitting a portion of the data with a patch, testing the fit for satisfaction within a given tolerance, and subdividing the patch if th...
An Algorithmic Analysis of Multiquadratic and Semidefinite Programming Problems
, 1993
"... are addressed. Two algorithms are developed for certain feasibility versions of the SDP, and the rst of these is shown to have polynomial time complexity when the dimension of the matrix map involved is xed. The second algorithm is a globally convergent Newtonlike method applied to a leastsquares ..."
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Cited by 35 (4 self)
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are addressed. Two algorithms are developed for certain feasibility versions of the SDP, and the rst of these is shown to have polynomial time complexity when the dimension of the matrix map involved is xed. The second algorithm is a globally convergent Newtonlike method applied to a leastsquares penalty function. The problem of characterizing and identifying quadratic maps with convex images is analyzed from both structural and complexity theoretic points of view. Then a study is made of the geometry of a class of convex sets called spectrahedra, which are the feasible regions in semide nite programs. Finally, in Chapter 7, we develop some cutting plane techniques for MQP, based on eigenvalue inequalities. Acknowledgements I express my sincere gratitude to my thesis advisor Professor Alan Goldman for his support, ideas and encouragement. My special thanks to Professors Laszlo Lovasz and James Renegar for sparing their time generously and giving me very useful suggestions. I thank the warm and friendly Professors Dan Naiman and Ed Scheinerman for making my four year long stay at Johns Hopkins a very pleasant one. I am indebted to Prof. JongShi Pang and Prof. Roger Horn for giving a patient ear to many of my enthusiastic ideas and o ering suggestions. I also thank Prof. ShihPing Han for being a wonderful teacher, and Prof. Leslie Hall for being a patient second reader of my thesis. My interest in Multiquadratic Programming was initiated during my internship at AT&T Bell Laboratories in the summer of 1990, and I am obliged to Dr. Narendra Karmarkar for arranging this internship. I thank Dr. Farid Alizadeh, Dr. Florian Jarre, Profs. Raphael Loewy, Michael Overton and Stephen Vavasis for patiently answering my questions and sending me some literature. My heartfelt appreciation is due my parents, Lakshmi Pathy and Satyavathi, my sister,