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SODA
2012
ACM
196views Algorithms» more  SODA 2012»
9 years 9 months ago
Polytope approximation and the Mahler volume
The problem of approximating convex bodies by polytopes is an important and well studied problem. Given a convex body K in Rd , the objective is to minimize the number of vertices...
Sunil Arya, Guilherme Dias da Fonseca, David M. Mo...
IPL
2008
105views more  IPL 2008»
11 years 6 months ago
Hausdorff approximation of 3D convex polytopes
Let P be a convex polytope in Rd , d = 3 or 2, with n vertices. We present linear time algorithms for approximating P by simpler polytopes. For instance, one such algorithm select...
Mario A. Lopez, Shlomo Reisner
FLAIRS
2004
11 years 8 months ago
Blind Data Classification Using Hyper-Dimensional Convex Polytopes
A blind classification algorithm is presented that uses hyperdimensional geometric algorithms to locate a hypothesis, in the form of a convex polytope or hyper-sphere. The convex ...
Brent T. McBride, Gilbert L. Peterson
CONCUR
1993
Springer
11 years 10 months ago
Loop Parallelization in the Polytope Model
During the course of the last decade, a mathematical model for the parallelization of FOR-loops has become increasingly popular. In this model, a (perfect) nest of r FOR-loops is r...
Christian Lengauer
ICCAD
1993
IEEE
101views Hardware» more  ICCAD 1993»
11 years 10 months ago
Convexity-based algorithms for design centering
A new technique for design centering, and for polytope approximation of the feasible region for a design are presented. In the rst phase, the feasible region is approximated by a ...
Sachin S. Sapatnekar, Pravin M. Vaidya, Steve M. K...
COMPGEOM
2006
ACM
12 years 18 days ago
An optimal-time algorithm for shortest paths on a convex polytope in three dimensions
We present an optimal-time algorithm for computing (an implicit representation of) the shortest-path map from a fixed source s on the surface of a convex polytope P in three dime...
Yevgeny Schreiber, Micha Sharir
FOCS
2006
IEEE
12 years 20 days ago
On a Geometric Generalization of the Upper Bound Theorem
We prove an upper bound, tight up to a factor of 2, for the number of vertices of level at most in an arrangement of n halfspaces in Rd , for arbitrary n and d (in particular, the...
Uli Wagner
COMPGEOM
2009
ACM
12 years 1 months ago
Computing hereditary convex structures
Color red and blue the n vertices of a convex polytope P in R3 . Can we compute the convex hull of each color class in o(n log n)? What if we have χ > 2 colors? What if the co...
Bernard Chazelle, Wolfgang Mulzer
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