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.

Fundamental structures.- Static randomized incremental algorithms.- The Delaunay tree.- A general structure: The influence graph.- The k-Delaunay tree.- Towards a fully dynamic structure.- Parallel work.