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Complexity of iff. An (curved) edge: Vertices: Only

ACM SIGMOD–SIGACT–SIGART Symposium on PRINCIPLES OF DATABASE SYSTEMS (PODS 2013). Nearest-Neighbor Searching Under Uncertainty II. Probabilistic Nearest Neighbor (PNN). Motivation. Indexing schemes (using less space) If each uncertainty region is a disk ,

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Complexity of iff. An (curved) edge: Vertices: Only

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  1. ACM SIGMOD–SIGACT–SIGART Symposium on PRINCIPLES OF DATABASE SYSTEMS (PODS 2013) Nearest-Neighbor Searching Under Uncertainty II Probabilistic Nearest Neighbor (PNN) Motivation • Indexing schemes (using less space) • If each uncertainty region is a disk, • If each has possible locations, • Two sub-problems: • Nonzero NNs. • Nonzero Voronoi Diagram for any 𝒯⊆𝒫, • Computing • Data location is imprecise… • Sensor databases • Face recognition • Mobile data What is the“nearest neighbor” of 𝑞 now? Nearest Neighbor (NN) Searching Prior Work Computing Pankaj K. Agarwal, Boris Aronov, SarielHar-Peled, Jeff M. Phillips, Ke Yi, and Wuzhou Zhang • Nonzero NNs. • in the case of disks: [Evans et al. 2008] • Voronoi-based heuristics [Zhang et al. 2013] • Computing • Best-effort based [Kriegel et al. 2007][Cheng et al. 2008] • Other variants. • Expected Nearest Neighbor [Agarwal et al. 2012] • Superseding Nearest Neighbor [Yuen et al. 2010] • Top- NNs [Ljosa et al. 2007][Beskales et al. 2008] • Post • office • problem • 𝑆: a set of points • 𝑞: any query point • Find the closest one • Monte Carlo method The number of instantiations is . If each has a discrete pdf of size : , with probability at least • Spiral Search method • Only need to look at a small number of closest points! • Each has 𝑘 equally likely locations. • Estimate using 𝑚 closest points. • Independent of 𝑛! Model and Qualification Probability Nonzero NNs Uncertain point : represented as a probability density function in : the pdf of 𝑞: any given query point : the pdf of : the cdf of The qualification probability Complexity of iff. An (curved) edge: Vertices: Only Future Work • The PNN problem under the existential model • The non-zero NN definition does not make sense • Solutions here cannot be directly adapted Acknowledgements • Complexity of • if assuming general disks. • if pairwise disjoint disks of same radii. • if has locations. • In all the cases, • where , and is the output size. P. Agarwaland W. Zhang are supported by NSF under grants CCF-09-40671, CCF-10-12254, and CCF-11-61359, by ARO grants W911NF-07-1-0376 and W911NF-08-1-0452, and by an ERDC contract W9132V-11-C-0003. B. Aronovis supported by NSF grants CCF-08-30691, CCF-11-17336, and CCF-12-18791, and by NSA MSP Grant H98230-10-1-0210. S. Har-Peled is supported by NSF grants CCF-09-15984 and CCF-12-17462.

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