DCG
2008
13 years 4 months ago
2008
For convex bodies K with C2 boundary in Rd, we explore random polytopes with vertices chosen along the boundary of K. In particular, we determine asymptotic properties of the volum...
DCG
2008
13 years 4 months ago
2008
DCG
2008
13 years 4 months ago
2008
We prove Helly-type theorems for line transversals to disjoint unit balls in Rd . In particular, we show that a family of n 2d disjoint unit balls in Rd has a line transversal if,...
DCG
2008
13 years 4 months ago
2008
We define a centrally symmetric analogue of the cyclic polytope and study its facial structure. We conjecture that our polytopes provide asymptotically the largest number of faces...
DCG
2008
13 years 4 months ago
2008
Recently there has been a lot of interest in geometrically motivated approaches to data analysis in high dimensional spaces. We consider the case where data is drawn from sampling...
DCG
2008
13 years 4 months ago
2008
The crossing number of a graph is the minimum number of edge intersections in a plane drawing of a graph, where each intersection is counted separately. If instead we count the nu...
DCG
2008
13 years 4 months ago
2008
Two-dimensional constrained Delaunay triangulations are geometric structures that are popular for interpolation and mesh generation because they respect the shapes of planar domai...
DCG
2008
13 years 4 months ago
2008
We construct CW spheres from the lattices that arise as the closed sets of a convex closure, the meet-distributive lattices. These spheres are nearly polytopal, in the sense that t...
DCG
2008
13 years 4 months ago
2008
Let P be a set of n points in Rd . A subset S of P is called a (k, )-kernel if for every direction, the direction width of S -approximates that of P, when k "outliers" c...
DCG
2008
13 years 4 months ago
2008
We prove that for d 3, the 1-skeleton of any (d - 1)-dimensional doubly Cohen-Macaulay (abbreviated 2-CM) complex is generically drigid. This implies that Barnette's lower b...