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674
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
Testing halfspaces
 IN PROC. 20TH ANNUAL SYMPOSIUM ON DISCRETE ALGORITHMS (SODA
, 2009
"... This paper addresses the problem of testing whether a Booleanvalued function f is a halfspace, i.e. a function of the form f(x) = sgn(w ·x−θ). We consider halfspaces over the continuous domain R n (endowed with the standard multivariate Gaussian distribution) as well as halfspaces over the Boolean ..."
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Cited by 34 (15 self)
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other ingredients. These include “crossconsistency ” versions of the results mentioned above for pairs of halfspaces with the same weights but different thresholds; new structural results relating the largest degree1 Fourier coefficient and the largest weight in unbalanced halfspaces; and algorithmic
Mesh Generation And Optimal Triangulation
, 1992
"... We survey the computational geometry relevant to finite element mesh generation. We especially focus on optimal triangulations of geometric domains in two and threedimensions. An optimal triangulation is a partition of the domain into triangles or tetrahedra, that is best according to some cri ..."
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Cited by 213 (7 self)
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We survey the computational geometry relevant to finite element mesh generation. We especially focus on optimal triangulations of geometric domains in two and threedimensions. An optimal triangulation is a partition of the domain into triangles or tetrahedra, that is best according to some criterion that measures the size, shape, or number of triangles. We discuss algorithms both for the optimization of triangulations on a fixed set of vertices and for the placement of new vertices (Steiner points). We briefly survey the heuristic algorithms used in some practical mesh generators.
Spectral Partitioning Works: Planar graphs and finite element meshes
 In IEEE Symposium on Foundations of Computer Science
, 1996
"... Spectral partitioning methods use the Fiedler vectorthe eigenvector of the secondsmallest eigenvalue of the Laplacian matrixto find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extr ..."
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Cited by 199 (10 self)
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Spectral partitioning methods use the Fiedler vectorthe eigenvector of the secondsmallest eigenvalue of the Laplacian matrixto find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extremely well. In this paper, we show that spectral partitioning methods work well on boundeddegree planar graphs and finite element meshes the classes of graphs to which they are usually applied. While naive spectral bisection does not necessarily work, we prove that spectral partitioning techniques can be used to produce separators whose ratio of vertices removed to edges cut is O( p n) for boundeddegree planar graphs and twodimensional meshes and O i n 1=d j for wellshaped ddimensional meshes. The heart of our analysis is an upper bound on the secondsmallest eigenvalues of the Laplacian matrices of these graphs. 1. Introduction Spectral partitioning has become one of the mos...
Dissimilarity representations in pattern recognition. Concepts, theory and applications
, 2005
"... ..."
Fast Scenariobased Decision Making in Unbalanced Distribution Networks
"... Abstract—In this paper we consider the problem faced by a distribution network operator that is required to guarantee, with high probability, the satisfaction of operational constraints of the grid in the presence of stochastic disturbances caused by fluctuating loads and intermittent microgeneratio ..."
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Cited by 1 (1 self)
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Abstract—In this paper we consider the problem faced by a distribution network operator that is required to guarantee, with high probability, the satisfaction of operational constraints of the grid in the presence of stochastic disturbances caused by fluctuating loads and intermittent microgeneration. We formulate this problem as a chanceconstrained decision problem, and we employ a scenariobased approach in order to convert it into a largescale deterministic decision problem. In order to make this latter problem computationally tractable, we approximate the nonlinear power flow equations via a sparse, implicit linear model. This approach results in an accurate and fast decision making strategy, that we validate in simulations on the IEEE13 threephase test feeder. I.
Fluid Dynamics Averaging over Fast Gravity Waves for Geophysical Flows with Unbalanced Initial Data1
, 1997
"... Abstract. Various facets of recent mathematical theories for averaging over fast gravity waves on advective time scales for geophysical flows with unbalanced initial data are presented here including nonlinear Rossby adjustment and simplified reduced dynamics. This work is presented within the conte ..."
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Abstract. Various facets of recent mathematical theories for averaging over fast gravity waves on advective time scales for geophysical flows with unbalanced initial data are presented here including nonlinear Rossby adjustment and simplified reduced dynamics. This work is presented within
The History of Histograms (abridged)
 PROC. OF VLDB CONFERENCE
, 2003
"... The history of histograms is long and rich, full of detailed information in every step. It includes the course of histograms in diFFerent scientific fields, the successes and failures of histograms in approximating and compressing information, their adoption by industry, and solutions that hav ..."
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Cited by 113 (0 self)
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The history of histograms is long and rich, full of detailed information in every step. It includes the course of histograms in diFFerent scientific fields, the successes and failures of histograms in approximating and compressing information, their adoption by industry, and solutions that have been given on a great variety of histogramrelated problems. In this paper and in the same spirit of the histogram techniques themselves, we compress their entire history (including their "future history" as currently anticipated) in the given/fixed space budget, mostly recording details for the periods, events, and results with the highest (personallybiased) interest. In a limited set of experiments, the semantic distance between the compressed and the full form of the history was found relatively small!
Counting Solutions to Linear and Nonlinear Constraints through Ehrhart Polynomials: Applications to Analyze and Transform Scientific Programs
, 1996
"... In order to produce efficient parallel programs, optimizing compilers need to include an analysis of the initial sequential code. When analyzing loops with affine loop bounds, many computations are relevant to the same general problem: counting the number of integer solutions of selected free variab ..."
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Cited by 107 (0 self)
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In order to produce efficient parallel programs, optimizing compilers need to include an analysis of the initial sequential code. When analyzing loops with affine loop bounds, many computations are relevant to the same general problem: counting the number of integer solutions of selected free variables in a set of linear and/or nonlinear parameterized constraints. For example, computing the number of flops executed by a loop, of memory locations touched by a loop, of cache lines touched by a loop, or of array elements that need to be transmitted from a processor to another during the execution of a loop, is useful to determine if a loop is load balanced, evaluate message traffic and allocate message buffers. The objective of the presented method is to evaluate symbolically, in terms of symbolic constants (the size parameters) , this number of integer solutions. By modeling the considered counting problem as a union of rational convex polytopes, the number of included integer points is ...
A robust minimax approach to classification
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2002
"... When constructing a classifier, the probability of correct classification of future data points should be maximized. We consider a binary classification problem where the mean and covariance matrix of each class are assumed to be known. No further assumptions are made with respect to the classcondi ..."
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Cited by 102 (7 self)
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When constructing a classifier, the probability of correct classification of future data points should be maximized. We consider a binary classification problem where the mean and covariance matrix of each class are assumed to be known. No further assumptions are made with respect to the classconditional distributions. Misclassification probabilities are then controlled in a worstcase setting: that is, under all possible choices of classconditional densities with given mean and covariance matrix, we minimize the worstcase (maximum) probability of misclassification of future data points. For a linear decision boundary, this desideratum is translated in a very direct way into a (convex) second order cone optimization problem, with complexity similar to a support vector machine problem. The minimax problem can be interpreted geometrically as minimizing the maximum of the Mahalanobis distances to the two classes. We address the issue of robustness with respect to estimation errors (in the means and covariances of the
Results 1  10
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674