Results 1 
2 of
2
Polyhedral representation conversion up to symmetries
, 2009
"... We give a short survey on computational techniques which can be used to solve the representation conversion problem for polyhedra up to symmetries. In particular we discuss decomposition methods, which reduce the problem to a number of lower dimensional subproblems. These methods have been successfu ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
We give a short survey on computational techniques which can be used to solve the representation conversion problem for polyhedra up to symmetries. In particular we discuss decomposition methods, which reduce the problem to a number of lower dimensional subproblems. These methods have been successfully used by different authors in special contexts. Moreover, we sketch an incremental method, which is a generalization of Fourier–Motzkin elimination, and we give some ideas how symmetry can be exploited using pivots.
A New Approach to OutputSensitive Voronoi Diagrams
"... We describe a new algorithm for computing the Voronoi diagram of a set of n points in constantdimensional Euclidean space. The running time of our algorithm is O(f log n log ∆) where f is the output complexity of the Voronoi diagram and ∆ is the spread of the input, the ratio of largest to smallest ..."
Abstract
 Add to MetaCart
We describe a new algorithm for computing the Voronoi diagram of a set of n points in constantdimensional Euclidean space. The running time of our algorithm is O(f log n log ∆) where f is the output complexity of the Voronoi diagram and ∆ is the spread of the input, the ratio of largest to smallest pairwise distances. Despite the simplicity of the algorithm and its analysis, it improves on the state of the art for all inputs with polynomial spread and nearlinear output size. The key idea is to first build the Voronoi diagram of a superset of the input points using ideas from Voronoi refinement mesh generation. Then, the extra points are removed in a straightforward way that allows the total work to be bounded in terms of the output complexity, yielding the output sensitive bound. The removal only involves local flips and is inspired by kinetic data structures. 1