Simulation of random geometric structures

The complexity of geometric algorithms is often express in terms of the input size and sometimes of the output size, but the behavior of these algorithms may depend drastically on the geometric distribution of the input. The difference between the best-case and the worst-case can be important. An alternative is to analyze these algorithms under the hypothesis of a probabilistic distribution of the data. When the input is a point set, an easy probabilistic hypothesis is to consider that points are independently distributed under some law (Poisson distribution, uniform distribution. . . ), unfortunately this hypothesis of independance may be unsuitable for several applications. The use of non independent distribution is very difficult to analyze theoretically, thus having access to simulations of practical instances would be of tremendous help to guide the intuition and to lead to reasonable conjectures. Unfortunately, the generation of useful random instances is a difficult question in itself. We plan to attack three specific questions, as described below: simulation of geometric structures, of conditioned structures, and of dependent pointsets.