Probabilistic matching of solids in arbitrary dimension

We give simple probabilistic algorithms that approximately maximize the volume of overlap of two solid shapes under translations and rigid motions. The shapes are subsets of R, d ≥ 2. The algorithms approximate w.r.t. an prespecified additive error and succeed with high probability. Apart from measurability assumptions, we only require from the shapes that uniformly distributed random points can be generated. An important example are finite unions of simplices that have pairwise disjoint interiors.