Closest pair problems in very high dimensions

Piotr Indyk; Moshe Lewenstein; Ohad Lipsky; Ely Porat

doi:10.1007/978-3-540-27836-8_66

Closest pair problems in very high dimensions

Piotr Indyk, Moshe Lewenstein, Ohad Lipsky, Ely Porat

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

27 Scopus citations

Abstract

The problem of finding the closest pair among a collection of points in ℛ^d is a well-known problem. There are better-than-naive- solutions for constant d and approximate solutions in general. We propose the first better-than-naive-solutions for the problem for large d. In particular, we present algorithms for the metrics L₁ and L_∞ with running times of O(n^(ω+3)/2) and O(n^(ω+3)/2log D) respectively, where O(n^ω) is the running time of matrix multiplication and D is the diameter of the points.

Original language	English
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editors	Josep Díaz, Juhani Karhumäki, Arto Lepistö, Donald Sannella
Publisher	Springer Verlag
Pages	782-792
Number of pages	11
ISBN (Print)	3540228497
DOIs	https://doi.org/10.1007/978-3-540-27836-8_66
State	Published - 2004

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3142
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

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10.1007/978-3-540-27836-8_66

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Indyk, P., Lewenstein, M., Lipsky, O., & Porat, E. (2004). Closest pair problems in very high dimensions. In J. Díaz, J. Karhumäki, A. Lepistö, & D. Sannella (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 782-792). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3142). Springer Verlag. https://doi.org/10.1007/978-3-540-27836-8_66

Indyk, Piotr ; Lewenstein, Moshe ; Lipsky, Ohad et al. / Closest pair problems in very high dimensions. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). editor / Josep Díaz ; Juhani Karhumäki ; Arto Lepistö ; Donald Sannella. Springer Verlag, 2004. pp. 782-792 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Indyk, P, Lewenstein, M, Lipsky, O & Porat, E 2004, Closest pair problems in very high dimensions. in J Díaz, J Karhumäki, A Lepistö & D Sannella (eds), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3142, Springer Verlag, pp. 782-792. https://doi.org/10.1007/978-3-540-27836-8_66

Closest pair problems in very high dimensions. / Indyk, Piotr; Lewenstein, Moshe; Lipsky, Ohad et al.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). ed. / Josep Díaz; Juhani Karhumäki; Arto Lepistö; Donald Sannella. Springer Verlag, 2004. p. 782-792 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3142).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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Indyk P, Lewenstein M, Lipsky O, Porat E. Closest pair problems in very high dimensions. In Díaz J, Karhumäki J, Lepistö A, Sannella D, editors, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2004. p. 782-792. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-27836-8_66

Closest pair problems in very high dimensions

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