Towards Dynamic Randomized Algorithms in Computational Geometry

Monique Teillaud (auth.)3540575030, 9783540575030, 0387575030

Computational geometry concerns itself with designing and analyzing algorithms for solving geometric problems. The field has reached a high level of sophistication, and very complicated algorithms have been designed.However, it is also useful to develop more practical algorithms, so long as they are based on rigorous methods. One such method is the use of randomized algorithms. These algorithms have become more and more popular, turning into one of the hottest areas of recent years. Dynamic algorithms are particularly interesting because in practice the data of a problem are often acquired progressively. In this monograph the author studies the theoretical complexity and practical efficiency of randomized dynamic algorithms.

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Table of contents :
Fundamental structures….Pages 6-19
Static randomized incremental algorithms….Pages 22-34
The Delaunay tree….Pages 36-43
A general structure: The influence graph….Pages 46-76
The k -Delaunay tree….Pages 78-107
Towards a fully dynamic structure….Pages 110-136
Parallel work….Pages 138-143