Epsilon geometry: building robust algorithms from imprecise computations
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
On linear-time deterministic algorithms for optimization problems in fixed dimension
Journal of Algorithms
Improved bounds on the sample complexity of learning
Journal of Computer and System Sciences
A Combinatorial Bound for Linear Programming and Related Problems
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
Almost-Delaunay simplices: nearest neighbor relations for imprecise points
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Uncertainty-aware and coverage-oriented deployment for sensor networks
Journal of Parallel and Distributed Computing
Indexing multi-dimensional uncertain data with arbitrary probability density functions
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Efficient query evaluation on probabilistic databases
The VLDB Journal — The International Journal on Very Large Data Bases
Approximation algorithms for clustering uncertain data
Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Algorithms for ε-Approximations of Terrains
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Triangulating input-constrained planar point sets
Information Processing Letters
Histograms and Wavelets on Probabilistic Data
ICDE '09 Proceedings of the 2009 IEEE International Conference on Data Engineering
Largest bounding box, smallest diameter, and related problems on imprecise points
Computational Geometry: Theory and Applications
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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.