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Geometric Computations on Indecisive and Uncertain Points
"... 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 p ..."
Abstract

Cited by 3 (1 self)
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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 shapefitting 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 LPtype 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. 1
Range Counting Coresets for Uncertain Data
, 2013
"... We study coresets for various types of range counting queries on uncertain data. In our model each uncertain point has a probability density describing its location, sometimes defined as k distinct locations. Our goal is to construct a subset of the uncertain points, including their locational uncer ..."
Abstract

Cited by 2 (1 self)
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We study coresets for various types of range counting queries on uncertain data. In our model each uncertain point has a probability density describing its location, sometimes defined as k distinct locations. Our goal is to construct a subset of the uncertain points, including their locational uncertainty, so that range counting queries can be answered by just examining this subset. We study three distinct types of queries. RE queries return the expected number of points in a query range. RC queries return the number of points in the range with probability at least a threshold. RQ queries returns the probability that fewer than some threshold fraction of the points are in the range. In both RC and RQ coresets the threshold is provided as part of the query. And for each type of query we provide coreset constructions with approximationsize tradeoffs. We show that random sampling can be used to construct each type of coreset, and we also provide significantly improved bounds using discrepancybased approaches on axisaligned range queries.