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Physical Sciences and Mathematics Commons™
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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Fast Implementation Of Depth Contours Using Topological Sweep, Kim Miller, Suneeta Ramaswami, Peter Rousseeuw, Toni Sellarès, Diane Souvaine, Ileana Streinu, Anja Struyf
Fast Implementation Of Depth Contours Using Topological Sweep, Kim Miller, Suneeta Ramaswami, Peter Rousseeuw, Toni Sellarès, Diane Souvaine, Ileana Streinu, Anja Struyf
Computer Science: Faculty Publications
The concept of location depth was introduced in statistics as a way to extend the univariate notion of ranking to a bivariate configuration of data points. It has been used successfully for robust estimation, hypothesis testing, and graphical display. These reguire the computation of depth regions, which form a collection of nested polygons. The center of the deepest region is called the Tukey median. The only available implemented algorithms for the depth contours and the Tukey median are slow, which limits their usefulness. In this paper we describe an optimal algorithm which computes all depth contours in &Ogr;(n 2) time …
Polygonal Chains Cannot Lock In 4d, Roxana Cocan, Joseph O'Rourke
Polygonal Chains Cannot Lock In 4d, Roxana Cocan, Joseph O'Rourke
Computer Science: Faculty Publications
We prove that, in all dimensions d ≥ 4, every simple open polygonal chain and every tree may be straightened, and every simple closed polygonal chain may be convexified. These reconfigurations can be achieved by algorithms that use polynomial time in the number of vertices, and result in a polynomial number of “moves.” These results contrast to those known for d = 2, where trees can “lock,” and for d = 3, where open and closed chains can lock.
Computational Geometry Column 42, Joseph S. B. Mitchell, Joseph O'Rourke
Computational Geometry Column 42, Joseph S. B. Mitchell, Joseph O'Rourke
Computer Science: Faculty Publications
A compendium of thirty previously published open problems in computational geometry is presented.
Computational Geometry Column 41, Joseph O'Rourke
Computational Geometry Column 41, Joseph O'Rourke
Computer Science: Faculty Publications
The recent result that n congruent balls in Rd have at most 4 distinct geometric permutations is described.
On The Folkman-Lawrence Topological Representation Theorem For Oriented Matroids Of Rank 3, Jürgen Bokowski, Susanne Mock, Ileana Streinu
On The Folkman-Lawrence Topological Representation Theorem For Oriented Matroids Of Rank 3, Jürgen Bokowski, Susanne Mock, Ileana Streinu
Computer Science: Faculty Publications
We present a new direct proof of the Folkman-Lawrence topological representation theorem for oriented matroids of rank 3. © 2001 Academic Press.