K. Mulmuley, "Computational Geometry", Prentice Hall, 1994 Home/Search Document Not in Database Summary Related Articles Check |
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Visibility Line in a Direction for a Set of Parallel Line.. - Litiu, Kountanis (Correct)
....The worst possible configuration of the line segments is determined to be a staircase arrangement with a garbage collection segment. keywords: visibility, staircase, garbage collector 1 Introduction Visibility and related problems have been the subject of intense study in computational geometry [1, 3, 7]. These problems can be classified into two wide categories: visibility from a point and visibility in a direction. The two categories are further divided into sub categories depending on the objects in the domain of the problem, for example, intersecting or non intersecting line segments, simple ....
K. Mulmuley, "Computational Geometry", Prentice Hall, 1994
Reductions Among High Dimensional Proximity Problems - Goel, Indyk, Varadarajan (2000) (5 citations) (Correct)
....closest pair problem, furthest pair (or diameter) problem, many variants of clustering (including MST) and nearest neighbor search all belong to this class. If the dimension d is low, these problems enjoy very efficient (exact or approximate) solutions (e.g. see [29, 4, 26, 1] or the textbooks [28, 27]) However, the running time and or space requirements of these algorithms grow exponentially with the dimension. This is unfortunate, since the high dimensional versions of the above problems are of major and growing importance to a variety of applications, usually involving similarity search or ....
K. Mulmuley, "Computational geometry", Prentice Hall, 1993.
The Quickhull Algorithm for Convex Hulls - Barber, Dobkin, Huhdanpaa (1996) (89 citations) (Correct)
....of the halfspaces. Recent work on convex hulls and Delaunay triangulations has focused on variations of a randomized, incremental algorithm that has optimal expected performance [Chazelle and Matousek 1992] Clarkson et al. 1993] Edelsbrunner and Shah 1992] Guibas et al. 1992] Joe 1991] [Mulmuley 1994]. Points are processed one at a time in a random order. In this article, we propose and analyze a strategy for processing points in a more efficient order. The result is a faster algorithm for distributions with interior points. An incremental algorithm for the convex hull repeatedly adds a point ....
Mulmuley, K. 1994. Computational Geometry, An Introduction Through Randomized Algorithms. Prentice-Hall.
Speeding Up An Algorithm For Checking Robust Stability Of.. - Garloff, Graf, Zettler (1998) (Correct)
....2 Ug contains the origin. By expanding p e (x) and p o (x) simultaneously into their Bernstein forms one obtains a set of points (b (e) I (U ) b (o) I (U ) in the plane, denoted by b I (U ) Then one computes their convex hull what can be done in optimal time using O( log ) operations, e.g. (Mulmuley, 1994; Preparata and Shamos, 1990) where denotes the number of points. Then one checks whether the origin of the plane is contained in the convex hull since Conv P(U ) Conv B(U ) holds true. If it is outside, the family of polynomials is robustly stable. Otherwise an inclusion test given by ....
Mulmuley, K. (1994). Computational Geometry, An Introduction through Randomized Algorithms. Prentice Hall, Englewood-Cliffs.
Dimensionality Reduction Techniques for Proximity Problems - Indyk (2000) (5 citations) (Correct)
....problems which involve the notion of a distance between points in a d dimensional space. For example, the closest pair problem, furthest pair (or diameter) problem and nearest neighbor search all belong to this class. If the dimension d is low, these problems have very efficient solutions [13, 3, 12]. However, the running time and or space requirements of these algorithms grow exponentially with the dimension. This is unfortunate, since the high dimensional versions of the above problems are of major and growing importance to a variety of applications, usually involving similarity search or ....
K. Mulmuley, "Computational geometry", Prentice Hall, 1993.
Experiments with Computing Geometric Minimum Spanning Trees.. - Narasimhan, al. (1999) (2 citations) (Correct)
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K. Mulmuley. Computational Geometry. Prentice Hall, 1994.
Teaching Computational Geometry - Overmars (1993) (Correct)
No context found.
Mulmuley, K. 1993 Computational Geometry, An Introduction Through Randomized Algorithms, Prentice Hall, Englewood Cliffs, New Jersey, U.S.A.
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