NDLI: Efficient regular data structures and algorithms for location and proximity problems

Content Provider	IEEE Xplore Digital Library
Author	Amir, A. Efrat, A. Indyk, P. Samet, H.
Copyright Year	1999
Description	Author affiliation: IBM Almaden Res. Center, San Jose, CA, USA (Amir, A.)
Abstract	Investigates data structures obtained by a recursive partitioning of the input domain into regions of equal size. One of the most well-known examples of such a structure is the quadtree, which is used in this paper as a basis for more complex data structures; we also provide multidimensional versions of the stratified tree of P. van Emde Boas (1997). We show that, under the assumption that the input points have limited precision (i.e. are drawn from an integer grid of size u), these data structures yield efficient solutions to many important problems. In particular, they allow us to achieve O(log log u) time per operation for finding the dynamic approximate nearest neighbor (under insertions and deletions) and the exact online closest pair (under insertions only) in any constant dimension. They allow O(log log u) point location in a given planar shape or in its expansion (dilation by a ball of a given radius). Finally, we provide a linear-time (optimal) algorithm for computing the expansion of a shape represented by a quadtree. This result shows that the spatial order imposed by this regular data structure is sufficient to optimize the dilation by a ball operation.
Starting Page	160
Ending Page	170
File Size	353174
Page Count	11
File Format	PDF
ISBN	0769504094
ISSN	02725428
DOI	10.1109/SFFCS.1999.814588
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1999-10-17
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Data structures Shape Computer science Tree data structures Multidimensional systems Partitioning algorithms Nearest neighbor searches Educational institutions Contracts Data processing
Content Type	Text
Resource Type	Article

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