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80
On approximating the depth and related problems
 SIAM J. Comput
"... We study the question of finding a deepest point in an arrangement of regions, and provide a fast algorithm for this problem using random sampling, showing it sufficient to solve this problem when the deepest point is shallow. This implies, among other results, a fast algorithm for solving linear pr ..."
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Cited by 63 (11 self)
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We study the question of finding a deepest point in an arrangement of regions, and provide a fast algorithm for this problem using random sampling, showing it sufficient to solve this problem when the deepest point is shallow. This implies, among other results, a fast algorithm for solving linear programming with violations approximately. We also use this technique to approximate the disk covering the largest number of red points, while avoiding all the blue points, given two such sets in the plane. Using similar techniques imply that approximate range counting queries have roughly the same time and space complexity as emptiness range queries. 1
On Bregman Voronoi Diagrams
 in "Proc. 18th ACMSIAM Sympos. Discrete Algorithms
, 2007
"... The Voronoi diagram of a point set is a fundamental geometric structure that partitions the space into elementary regions of influence defining a discrete proximity graph and dually a wellshaped Delaunay triangulation. In this paper, we investigate a framework for defining and building the Voronoi ..."
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Cited by 42 (22 self)
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The Voronoi diagram of a point set is a fundamental geometric structure that partitions the space into elementary regions of influence defining a discrete proximity graph and dually a wellshaped Delaunay triangulation. In this paper, we investigate a framework for defining and building the Voronoi diagrams for a broad class of distortion measures called Bregman divergences, that includes not only the traditional (squared) Euclidean distance, but also various divergence measures based on entropic functions. As a byproduct, Bregman Voronoi diagrams allow one to define informationtheoretic Voronoi diagrams in statistical parametric spaces based on the relative entropy of distributions. We show that for a given Bregman divergence, one can define several types of Voronoi diagrams related to each other
The 3D Visibility Complex
, 2002
"... this paper, we present a theoretical study of 3D visibility properties for scenes of smooth convex objects ..."
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Cited by 42 (0 self)
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this paper, we present a theoretical study of 3D visibility properties for scenes of smooth convex objects
The Design and Implementation of Planar Maps in CGAL
 Special Issue, selected papers of the Workshop on Algorithm Engineering (WAE
, 1999
"... this paper has been supported in part by ESPRIT IV LTR Projects No. 21957 (CGAL) and No. 28155 (GALIA), by the USAIsrael Binational Science Foundation, by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities (Center for Geometric Computing and its Applications), by ..."
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Cited by 39 (17 self)
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this paper has been supported in part by ESPRIT IV LTR Projects No. 21957 (CGAL) and No. 28155 (GALIA), by the USAIsrael Binational Science Foundation, by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities (Center for Geometric Computing and its Applications), by a FrancoIsraeli research grant "factory of the future" (monitored by AFIRST/France and The Israeli Ministry of Science), and by the Hermann Minkowski  Minerva Center for Geometry at Tel Aviv University
Crowd of virtual humans: a new approach for real time navigation in complex and structured environments
 Computer Graphics Forum
, 2004
"... The navigation activity is an every day practice for any human being capable of locomotion. Our objective in this work is to reproduce this crucial human activity inside virtual environments. Putting together the high complexity of a realistic environment such as a city, a big amount of virtual huma ..."
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Cited by 38 (0 self)
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The navigation activity is an every day practice for any human being capable of locomotion. Our objective in this work is to reproduce this crucial human activity inside virtual environments. Putting together the high complexity of a realistic environment such as a city, a big amount of virtual humans and the realtime constraint requires to optimize each aspect of the animation process. In this paper, we present a suitable topological structuring of the geometric environment to allow fast path finding as well as an efficient reactive navigation algorithm for virtual humans evolving inside a crowd. 1.
An experimental analysis of selfadjusting computation
 In Proceedings of the ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI
, 2006
"... Selfadjusting computation uses a combination of dynamic dependence graphs and memoization to efficiently update the output of a program as the input changes incrementally or dynamically over time. Related work showed various theoretical results, indicating that the approach can be effective for a r ..."
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Cited by 35 (19 self)
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Selfadjusting computation uses a combination of dynamic dependence graphs and memoization to efficiently update the output of a program as the input changes incrementally or dynamically over time. Related work showed various theoretical results, indicating that the approach can be effective for a reasonably broad range of applications. In this article, we describe algorithms and implementation techniques to realize selfadjusting computation and present an experimental evaluation of the proposed approach on a variety of applications, ranging from simple list primitives to more sophisticated computational geometry algorithms. The results of the experiments show that the approach is effective in practice, often offering orders of magnitude speedup from recomputing the output from scratch. We believe this is the first experimental evidence that incremental computation of any type is effective in practice for a reasonably broad set of applications.
Isotropic Surface Remeshing
, 2003
"... This paper proposes a new method for isotropic remeshing of triangulated surface meshes. Given a triangulated surface mesh to be resampled and a userspecified density function defined over it, we first distribute the desired number of samples by generalizing error diffusion, commonly used in image ..."
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Cited by 31 (3 self)
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This paper proposes a new method for isotropic remeshing of triangulated surface meshes. Given a triangulated surface mesh to be resampled and a userspecified density function defined over it, we first distribute the desired number of samples by generalizing error diffusion, commonly used in image halftoning, to work directly on mesh triangles and feature edges. We then use the resulting sampling as an initial configuration for building a weighted centroidal Voronoi tessellation in a conformal parameter space, where the specified density function is used for weighting. We finally create the mesh by lifting the corresponding constrained Delaunay triangulation from parameter space. A precise control over the sampling is obtained through a flexible design of the density function, the latter being possibly lowpass filtered to obtain a smoother gradation. We demonstrate the versatility of our approach through various remeshing examples.
Taking a Walk in a Planar Arrangement
 SIAM J. Comput
, 1999
"... We present a new randomized algorithm for computing portions of an arrangement of n arcs in the plane, each pair of which intersect in at most t points. We use this algorithm to perform online walks inside such an arrangement (i.e., compute all the faces that a curve crosses, where the curve is g ..."
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Cited by 26 (6 self)
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We present a new randomized algorithm for computing portions of an arrangement of n arcs in the plane, each pair of which intersect in at most t points. We use this algorithm to perform online walks inside such an arrangement (i.e., compute all the faces that a curve crosses, where the curve is given in an online manner), and to compute a level in an arrangement, both in an outputsensitive manner. The expected running time of the algorithm is O( t+2 (m+n) log n), where m is the number of intersections between the walk and the given arcs. No algorithm with similar performance is known for the general case of arcs. For the case of lines and segments, our algorithm improves the best known algorithm of [OvL81] by almost a logarithmic factor. 1 Introduction Let S be a set of n xmonotone arcs in the plane. Computing the whole (or parts of the) arrangement A( S), induced by the arcs of S, is one of the fundamental problems in computational geometry, and has received a lot o...
Selfimproving algorithms
 in SODA ’06: Proceedings of the seventeenth annual ACMSIAM symposium on Discrete algorithm
"... We investigate ways in which an algorithm can improve its expected performance by finetuning itself automatically with respect to an arbitrary, unknown input distribution. We give such selfimproving algorithms for sorting and computing Delaunay triangulations. The highlights of this work: (i) an al ..."
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Cited by 26 (4 self)
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We investigate ways in which an algorithm can improve its expected performance by finetuning itself automatically with respect to an arbitrary, unknown input distribution. We give such selfimproving algorithms for sorting and computing Delaunay triangulations. The highlights of this work: (i) an algorithm to sort a list of numbers with optimal expected limiting complexity; and (ii) an algorithm to compute the Delaunay triangulation of a set of points with optimal expected limiting complexity. In both cases, the algorithm begins with a training phase during which it adjusts itself to the input distribution, followed by a stationary regime in which the algorithm settles to its optimized incarnation. 1