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DCG
2006
110views more  DCG 2006»
13 years 7 months ago
High-Dimensional Centrally Symmetric Polytopes with Neighborliness Proportional to Dimension
Let A be a d by n matrix, d < n. Let C be the regular cross polytope (octahedron) in Rn . It has recently been shown that properties of the centrosymmetric polytope P = AC are ...
David L. Donoho
SAC
2010
ACM
14 years 2 months ago
Polytope-based computation of polynomial ranges
Polynomial ranges are commonly used for numerically solving polynomial systems with interval Newton solvers. Often ranges are computed using the convex hull property of the tensor...
Christoph Fünfzig, Dominique Michelucci, Sebt...
SMA
2010
ACM
171views Solid Modeling» more  SMA 2010»
13 years 7 months ago
Efficient simplex computation for fixture layout design
Designing a fixture layout of an object can be reduced to computing the largest simplex and the resulting simplex is classified using the radius of the largest inscribed ball cent...
Yu Zheng, Ming C. Lin, Dinesh Manocha
NIPS
2007
13 years 8 months ago
New Outer Bounds on the Marginal Polytope
We give a new class of outer bounds on the marginal polytope, and propose a cutting-plane algorithm for efficiently optimizing over these constraints. When combined with a concav...
David Sontag, Tommi Jaakkola
COMPGEOM
2009
ACM
14 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