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DCG
2010
97views more  DCG 2010»
11 years 10 months ago
Cech Type Approach to Computing Homology of Maps
A new approach to algorithmic computation of the homology of spaces and maps is presented. The key point of the approach is a change in the representation of sets. The proposed rep...
Marian Mrozek
DCG
2010
101views more  DCG 2010»
11 years 10 months ago
Unknot Diagrams Requiring a Quadratic Number of Reidemeister Moves to Untangle
Given any knot diagram E, we present a sequence of knot diagrams of the same knot type, for which the minimum number of Reidemeister moves required to pass to E is quadratic with ...
Joel Hass, Tahl Nowik
DCG
2008
86views more  DCG 2008»
11 years 11 months ago
Circle Patterns on Singular Surfaces
Jean-Marc Schlenker
DCG
2008
78views more  DCG 2008»
11 years 11 months ago
Self-Similar Tiling Systems, Topological Factors and Stretching Factors
In this paper we prove that if two self-similar tiling systems, with respective stretching factors 1 and 2, have a common factor which is a non periodic tiling system, then 1 and 2...
María Isabel Cortez, Fabien Durand
DCG
2008
101views more  DCG 2008»
11 years 11 months ago
On the Hardness of Computing Intersection, Union and Minkowski Sum of Polytopes
For polytopes P1, P2 Rd we consider the intersection P1 P2, the convex hull of the union CH(P1 P2), and the Minkowski sum P1 + P2. For Minkowski sum we prove that enumerating t...
Hans Raj Tiwary
DCG
2008
88views more  DCG 2008»
11 years 11 months ago
On the Number of Birch Partitions
Birch and Tverberg partitions are closely related concepts from discrete geometry. We show two properties for the number of Birch partitions: Evenness, and a lower bound. This imp...
Stephan Hell
DCG
2008
76views more  DCG 2008»
11 years 11 months ago
Asymmetry of Convex Polytopes and Vertex Index of Symmetric Convex Bodies
In [GL] it was shown that a polytope with few vertices is far from being symmetric in the Banach-Mazur distance. More precisely, it was shown that Banach-Mazur distance between su...
E. D. Gluskin, A. E. Litvak
DCG
2008
81views more  DCG 2008»
11 years 11 months ago
A Dense Packing of Regular Tetrahedra
We construct a dense packing of regular tetrahedra, with packing density D > .7786157. Keywords Crystallography
Elizabeth R. Chen
DCG
2008
80views more  DCG 2008»
11 years 11 months ago
Analysis of Incomplete Data and an Intrinsic-Dimension Helly Theorem
Jie Gao, Michael Langberg, Leonard J. Schulman
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