Download:
|
by Sunil Arya, Ho-yam Addy Fu
In Proceedings of the 11th ACM-SIAM Symposium on Discrete Algorithms
http://www.cs.ust.hk/faculty/arya/pub/exp.ps
Add To MetaCart
Abstract:
Most research in algorithms for geometric query problems has focused on their worstcase performance. But when information on the query distribution is available, the alternative paradigm of designing and analyzing algorithms from the perspective of expected-case performance appears more attractive. We study the approximate nearest neighbor problem from this point of view. As a first step in this direction, we assume that the query points are chosen uniformly from a hypercube that encloses all the data points; however, we make no assumption on the distribution of data points. We investigate three simple variants of partition trees: sliding-midpoint, balance-split, and hybrid-split trees. We show that with these simple tree-based data structures, it is possible to achieve linear space and logarithmic or polylogarithmic query time in the expected case. In contrast, the data structures known to achieve linear space and logarithmic query time in the worst case are complex, and algorithms on them run more slowly in practice. Moreover, for the sliding-midpoint tree, we prove that it achieves optimal expected query time under reasonable assumptions. 1
Citations
|
2961
|
Pattern Classification and Scene Analysis
– Duda, Hart
- 1973
|
|
2739
|
A mathematical theory of communication
– Shannon
- 1948
|
|
1460
|
Indexing by latent semantic analysis
– Deerwester, Dumais, et al.
- 1990
|
|
1097
|
Vector Quantization and Signal Compression
– Gersho, Gray
- 1992
|
|
681
|
W.: Query by Image and Video Content: The QBIC System
– Flickner, Sawhney, et al.
- 1997
|
|
566
|
O.: Computational Geometry. Algorithms and Applications
– Berg, Kreveld, et al.
- 2000
|
|
442
|
ªAn Optimal Algorithm for Approximate Nearest Neighbor Searching
– Arya, Mount, et al.
- 1994
|
|
410
|
An algorithm for finding best matches in logarithmic expected time
– Friedman, Bentley, et al.
- 1977
|
|
316
|
Approximate nearest neighbors: towards removing the curse of dimensionality
– Indyk, Motwani
- 1998
|
|
183
|
A Decomposition of Multi-Dimensional Point-Sets with Applications to kNearest-Neighbors and n-Body Potential Fields
– Callahan, Kosaraju
|
|
134
|
Two algorithms for nearest-neighbor search in high dimensions
– KLEINBERG
- 1997
|
|
130
|
Efficient search for approximate nearest neighbor in high dimensional spaces
– Kushilevitz, Ostrovsky, et al.
- 1998
|
|
67
|
An algorithm for approximate closest-point queries
– Clarkson
- 1994
|
|
61
|
S.: Ann: A library for approximate nearest neighbor searching
– MOUNT, ARYA
- 1997
|
|
57
|
Approximate nearest neighbor queries in fixed dimensions
– Arya, Mount
- 1993
|
|
49
|
Algorithms for fast vector quantization
– Arya, Mount
- 1993
|
|
43
|
Balanced aspect ratio trees: combining the advantages of k-d trees and octrees
– Duncan, Goodrich, et al.
- 1999
|
|
42
|
Approximate closest-point queries in high dimensions
– Bern
- 1993
|
|
38
|
Approximate nearest neighbor queries revisited
– Chan
- 1997
|
|
28
|
Linear-size approximate voronoi diagrams
– Arya, Malamatos
- 2002
|
|
15
|
Modestino. Rate-distortion performance of DPCM schemes for autoregressive sources
– Farvardin, W
- 1985
|
|
12
|
Analysis of approximate nearest neighbor searching with clustered point sets
– Maneewongvatana, Mount
- 1999
|
|
11
|
Efficient expected-case algorithms for planar point location
– Arya, Cheng, et al.
- 2000
|
|
6
|
It’s okay to be skinny, if your friends are fat
– Maneewongvatana, Mount
- 1999
|
|
2
|
Sorting and Searching. The Art of Computer Programming 3
– Knuth
- 1998
|
|
1
|
Expected-case complexity of planar point location. Unpublished manuscript
– Arya, Cheng, et al.
- 1999
|
