Nesterov and Todd discuss several path-following and potential-reduction 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 predictor-corrector steps in this framework. We also provide some computational results suggesting that our algorithm is more robust than alternative methods.

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 performance-critical 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 domain-specific mathematical structure of transform algorithms to implement a feedback-driven 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.

The main contributions of this paper are two-fold. 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 time-reversible. Our approximation to the steady state buffer distribution is called "Chernoff-Dominant Eigenvalue" since one parameter is obtained from Chernoff's theorem and t...

. 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...

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 three-step 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

Abstract—This paper presents a behavior-based 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.

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.

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...

This paper presents a new computational method for steady state analysis of finite QBDprocess with level-dependent transitions. The QBD state space is defined in two-dimension with N phases and K levels. Instead of formulating solutions in matrix-geometric form, the Foldingalgorithm provides a technique for direct computation of ßP = 0, where P is the QBD generator which is an (NK) \Theta (NK) matrix. Taking a finite sequence of fixed-cost binary reduction steps, the K-level matrix P is eventually reduced to a single-level matrix, from which a boundary vector is obtained. Each step halves the matrix size but keeps the QBD form. The solution ß is expressed as a product of the boundary vector and a finite sequence of expansion factors. The time and space complexity for solving ßP = 0 is therefore reduced from O(N 3 K) and O(N 2 K) to O(N 3 log 2 K)andO(N 2 log 2 K), respectively. The Folding-algorithm has a number of highly desirable advantages when it is applied to queueing an...

We describe a new convex quadratic programming bound for the quadratic assignment problem (QAP). The construction of the bound uses a semidefinite programming representation of a basic eigenvalue bound for QAP. The new bound dominates the well-known projected eigenvalue bound, and appears to be competitive with existing bounds in the tradeoff between bound quality and computational effort. Keywords: Quadratic Assignment Problem, Eigenvalue Bounds, Quadratic Programming, Semidefinite Programming. Dept. of Management Sciences, University of Iowa, Iowa City, IA 52242 y Dept. of Computer Science, University of Iowa, Iowa City, IA 52242 1 Introduction The quadratic assignment problem (QAP) in "Koopmans-Beckmann" form can be written QAP(A;B;C) : min tr(AXB + C)X T s:t: X 2 \Pi; where A, B and C are n \Theta n matrices, tr denotes the trace of a matrix, and \Pi is the set of n \Theta n permutation matrices. Throughout we assume that A and B are symmetric. The QAP is a very well-know...