Uncertainty envelopes

We introduce a new class of problems: computing the set of all the convex combinations of sites when their position is uncertain and depends linearly on shared parameters which vary according to a uniform distribution. The boundary of the set, called the uncertainty envelope, is useful in optimizing processes where there is uncertainty on the site positions and the objective functions. We provide upper bounds on the combinatorial complexity of the uncertainty envelope, and present the first efficient algorithm for its computation in the general case.