A General Randomized Incremental Reconstruction Procedure

The technique of randomized incremental construction allows a variety of geometric structures to be built quickly. This note shows that once such a structure is built, it is possible to store the geometric input data for it so that the structure can be built again by a randomized algorithm even more quickly. Except for the randomization, this generalizes the technique of Snoeyink and van Kreveld that applies to planar problems.