Geometric Computations on Indecisive and Uncertain Points
Abstract
We study computing geometric problems on uncertain points. An uncertain point is a point that does not have a fixed location, but rather is described by a probability distribution. When these probability distributions are restricted to a finite number of locations, the points are called indecisive points. In particular, we focus on geometric shape-fitting problems and on building compact distributions to describe how the solutions to these problems vary with respect to the uncertainty in the points. Our main results are: (1) a simple and efficient randomized approximation algorithm for calculating the distribution of any statistic on uncertain data sets; (2) a polynomial, deterministic and exact algorithm for computing the distribution of answers for any LP-type problem on an indecisive point set; and (3) the development of shape inclusion probability (SIP) functions which captures the ambient distribution of shapes fit to uncertain or indecisive point sets and are admissible to the two algorithmic constructions.
Cite
@article{arxiv.1205.0273,
title = {Geometric Computations on Indecisive and Uncertain Points},
author = {Allan Jorgensen and Maarten Löffler and Jeff M. Phillips},
journal= {arXiv preprint arXiv:1205.0273},
year = {2012}
}
Comments
26 pages, 30 figures. This replaces a paper here (http://arXiv.org/abs/0812.2967) that was split, extended, and published in two venues (ESA 2009 and WADS 2011); although the old version contains some minor content that was omitted to make a more coherent story