SODA
2012
ACM
11 years 7 months ago
2012
ACM
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...
ORL
2011
12 years 11 months ago
2011
The Chv´atal-Gomory closure and the split closure of a rational polyhedron are rational polyhedra. It was recently shown that the Chv´atal-Gomory closure of a strictly convex bo...
DM
2011
12 years 11 months ago
2011
Minkowski’s second theorem on successive minima gives an upper bound on the volume of a convex body in terms of its successive minima. We study the problem to generalize Minkowsk...
CCCG
2010
13 years 6 months ago
2010
A random polygon is the convex hull of uniformly distributed random points in a convex body K R2 . General upper bounds are established for the variance of the area of a random p...
ESA
2009
Springer
13 years 11 months ago
2009
Springer
According to a classical result of Gr¨unbaum, the transversal number τ(F) of any family F of pairwise-intersecting translates or homothets of a convex body C in Rd is bounded by...
STOC
2004
ACM
14 years 4 months ago
2004
ACM
We show that the hit-and-run random walk mixes rapidly starting from any interior point of a convex body. This is the first random walk known to have this property. In contrast, t...