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Davenport-Schinzel sequences and their geometric applications
An $(n,s)$ Davenport--Schinzel sequence, for positive integers $n$ and $s$, is a sequence composed of $n$ symbols with the properties that no two adjacent elements are equal, and that it does notExpand
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A Monte Carlo algorithm for fast projective clustering
We propose a mathematical formulation for the notion of optimal projective cluster, starting from natural requirements on the density of points in subspaces. This allows us to develop a Monte CarloExpand
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Approximating extent measures of points
We present a general technique for approximating various descriptors of the extent of a set <i>P</i> of <i>n</i> points in R<sup><i>d</i></sup> when the dimension <i>d</i> is an arbitrary fixedExpand
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Geometric Range Searching and Its Relatives
About ten years ago, the eld of range searching, especially simplex range searching, was wide open. At that time, neither e cient algorithms nor nontrivial lower bounds were known for mostExpand
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Handbook of Discrete and Computational Geometry
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On range searching with semialgebraic sets
LetP be a set ofn points in ℝd (whered is a small fixed positive integer), and let Γ be a collection of subsets of ℝd, each of which is defined by a constant number of bounded degree polynomialExpand
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Efficient algorithms for geometric optimization
We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametricExpand
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Label placement by maximum independent set in rectangles
Motivated by the problem of labeling maps, we investigate the problem of computing a large non-intersecting subset in a set of n rectangles in the plane. Our results are as follows. In O(n log n)Expand
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Simplification envelopes
We propose the idea of simplification envelopes for generating a hierarchy of level-of-detail approximations for a given polygonal model. Our approach guarantees that all points of an approximationExpand
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