Geometric Computations on Indecisive Points

We study computing with indecisive point sets. Such points have spatial uncertainty where the true location is one of a finite number of possible locations. This data arises from probing distributions a few times or when the location is one of a few locations from a known database. In particular, we study computing distributions of geometric functions such as the radius of the smallest enclosing ball and the diameter. Surprisingly, we can compute the distribution of the radius of the smallest enclosing ball exactly in polynomial time, but computing the same distribution for the diameter is #P-hard. We generalize our polynomial-time algorithm to all LP-type problems. We also utilize our indecisive framework to deterministically and approximately compute on a more general class of uncertain data where the location of each point is given by a probability distribution. ∗The second author is funded by NWO under the GOGO project and the Office of Naval Research under grant N00014-08-11015; the third author is supported by a subaward to the University of Utah under NSF award 0937060 to CRA.