Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Fast Approximation of Centrality and Distances in Hyperbolic Graphs Read chapter Read first chapter

2018 | OriginalPaper | Chapter

An Algorithm for Reducing Approximate Nearest Neighbor to Approximate Near Neighbor with \(O(\log {n})\) Query Time

Authors : Hengzhao Ma, Jianzhong Li

Published in: Combinatorial Optimization and Applications

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This paper proposes a new algorithm for reducing Approximate Nearest Neighbor problem to Approximate Near Neighbor problem. The advantage of this algorithm is that it achieves \(O(\log {n})\) query time. As a reduction problem, the query time complexity is the times of invoking the algorithm for Approximate Near Neighbor problem. All former algorithms for the same reduction need polylog(n) query time. A box split method proposed by Vaidya is used in our paper to achieve the \(O(\log {n})\) query time complexity.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Heuristics for the Score-Constrained Strip-Packing Problem
next chapter Exact and Approximate Map-Reduce Algorithms for Convex Hull
Footnotes
1
The deterministic one has exponential dependence on d, so it it rarely used in theory and practice.
 
2
It can be verified that, as long as \(r\ge Est(\mathfrak {b})\) is satisfied, the value of r doesn’t influence the value of \(Est(\mathfrak {b})\). The specific value of r will be shown latter.
 
Literature
1.
Andoni, A., Indyk, P.: Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions. In: 47th Annual IEEE Symposium on Foundations of Computer Science, vol. 51, pp. 459–468 (2006)
2.
Andoni, A., Indyk, P.: Nearest neighbors in high-dimensional spaces. In: Handbook of Discrete and Computational Geometry, 3rd edn, chap. 43, pp. 1135–1155. CRC Press Inc., Boca Raton (2017)
3.
Andoni, A., Razenshteyn, I.: Optimal data-dependent hashing for approximate near neighbors. In: Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing, pp. 793–801 (2015)
4.
Arya, S., Mount, D.M.: Approximate nearest neighbor queries in fixed dimensions. In: Proceedings of the Fourth Annual Symposium on Discrete Algorithms, pp. 271–280 (1993)
5.
Arya, S., Mount, D.M., Netanyahu, N.S., Silverman, R., Wu, A.Y.: An optimal algorithm for approximate nearest neighbor searching fixed dimensions. J. ACM 45(6), 891–923 (1998)MathSciNetCrossRef
6.
7.
Callahan, P.B., Kosaraju, S.R.: A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields. J. ACM 42(1), 67–90 (1995)MathSciNetCrossRef
8.
Chan, T.M.: Approximate nearest neighbor queries revisited. In: Proceedings of the Thirteenth Annual Symposium on Computational Geometry, vol. 20, pp. 352–358 (1997)
9.
Datar, M., Immorlica, N., Indyk, P., Mirrokni, V.S.: Locality-sensitive hashing scheme based on p-table distributions. In: Proceedings of the Twentieth annual Symposium on Computational Geometry, pp. 253–262 (2004)
10.
Feder, T., Greene, D.: Optimal algorithms for approximate clustering. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, pp. 434–444 (1988)
11.
Goel, A., Indyk, P., Varadarajan, K.: Reductions among high dimensional proximity problems. In: Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 769–778 (2001)
12.
Har-Peled, S.: A replacement for voronoi diagrams of near linear size. In: 42nd Annual IEEE Symposium on Foundations of Computer Science, pp. 94–103 (2001)
13.
Har-Peled, S., Indyk, P., Motwani, R.: Approximate nearest neighbor: towards removing the curse of dimensionality. Theory Comput. 8(1), 321–350 (2012)MathSciNetCrossRef
14.
Indyk, P., Motwani, R.: Approximate nearest neighbors: towards removing the curse of dimensionality. In: Proceedings of the Thirteenth Annual ACM Symposium on Theory of Computing, pp. 604–613 (1998)
15.
Kleinberg, J.M.: Two algorithms for nearest-neighbor search in high dimensions. In: Proceedings of the Twenty-ninth Annual ACM Symposium on Theory of Computing, pp. 599–608 (1997)
16.
Krauthgamer, R., Lee, J.R.: Navigating nets: simple algorithms for proximity search. In: Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 798–807 (2004)
17.
Kushilevitz, E., Ostrovsky, R., Rabani, Y.: Efficient search for approximate nearest neighbor in high dimensional spaces. SIAM J. Comput. 30(2), 457–474 (2000)MathSciNetCrossRef
18.
19.
Panigrahy, R.: Entropy based nearest neighbor search in high dimensions. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1186–1195 (2006)
20.
Vaidya, P.M.: An optimal algorithm for the all-nearest-neighbors problem. In: 27th Annual Symposium on Foundations of Computer Science, pp. 117–122 (1986)
Metadata
Title
An Algorithm for Reducing Approximate Nearest Neighbor to Approximate Near Neighbor with Query Time
Authors
Hengzhao Ma
Jianzhong Li
Copyright Year
2018
Book
Combinatorial Optimization and Applications

Print ISBN: 978-3-030-04650-7

Electronic ISBN: 978-3-030-04651-4

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-030-04651-4_31

Premium Partner

    Image Credits