Applications of random sampling in computational geometry, II

New Applications of random Sampling in Computational Geometry

This paper gives several new demonstrations of the usefulness of random sampling techniques in computational geometry. One new algorithm creates a search structure for arrangements of hyperplanes by sampling the hyperplanes and using information from the resulting arrangement to divide and conquer. This algorithm requires O(s) expected preprocessing time to build a search structure for an arran...

Parleda: a Library for Parallel Processing in Computational Geometry Applications

ParLeda is a software library that provides the basic primitives needed for parallel implementation of computational geometry applications. It can also be used in implementing a parallel application that uses geometric data structures. The parallel model that we use is based on a new heterogeneous parallel model named HBSP, which is based on BSP and is introduced here. ParLeda uses two main lib...

Applications of Random Sampling to On-line Algorithms in Computational Geometry

This paper presents a general framework for the design and randomized analysis of geometric algorithms. These algorithms are on-line and the framework provides general bounds for their expected space and time complexities when averaging over all permutations of the input data. The method is general and can be applied to various geometric problems. The power of the technique is illustrated by ne...

Computational Geometry II

Teaching Computational Geometry, II

Abstract In the 1993 CCCG at Waterloo the speaker gave a talk on “Teaching Computational Geometry”. Since then textbooks have been published, the field has developed further, and extensive geometric software libraries have become available. How has this impacted teaching computational geometry? Are the issues still the same? Have the topics changed? Can the study of computational geometry be mo...