Document Open Access Logo

Robust Proximity Search for Balls Using Sublinear Space

Authors Sariel Har-Peled, Nirman Kumar

PDF
Thumbnail PDF

File

LIPIcs.FSTTCS.2014.315.pdf
  • Filesize: 0.49 MB
  • 12 pages

Document Identifiers

Author Details

Sariel Har-Peled
Nirman Kumar

Cite As Get BibTex

Sariel Har-Peled and Nirman Kumar. Robust Proximity Search for Balls Using Sublinear Space. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 315-326, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014) https://doi.org/10.4230/LIPIcs.FSTTCS.2014.315

Abstract

Given a set of n disjoint balls b_1, ..., b_n in R^d, we provide a data structure, of near linear size, that can answer (1 +- epsilon)-approximate k-th-nearest neighbor queries in O(log(n) + 1/epsilon^d) time, where k and epsilon are provided at query time. If k and epsilon are provided in advance, we provide a data structure to answer such queries, that requires (roughly) O(n/k) space; that is, the data structure has sublinear space requirement if k is sufficiently large.

Subject Classification

Keywords
  • Approximate Nearest neighbors
  • algorithms
  • data structures

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. A. Andoni and P. Indyk. Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions. Commun. ACM, 51(1):117-122, 2008. Google Scholar
  2. S. Arya and T. Malamatos. Linear-size approximate Voronoi diagrams. In Proc. 13th ACM-SIAM Symp. Discrete Algs., pages 147-155, 2002. Google Scholar
  3. S. Arya, T. Malamatos, and D. M. Mount. Space-time tradeoffs for approximate spherical range counting. In Proc. 16th ACM-SIAM Symp. Discrete Algs., pages 535-544, 2005. Google Scholar
  4. S. Arya, T. Malamatos, and D. M. Mount. Space-time tradeoffs for approximate nearest neighbor searching. J. Assoc. Comput. Mach., 57(1):1-54, 2009. Google Scholar
  5. S. Arya and D. M. Mount. Approximate range searching. Comput. Geom. Theory Appl., 17:135-152, 2000. Google Scholar
  6. S. Arya, D. M. Mount, N. S. Netanyahu, R. Silverman, and A. Y. Wu. An optimal algorithm for approximate nearest neighbor searching in fixed dimensions. J. Assoc. Comput. Mach., 45(6):891-923, 1998. Google Scholar
  7. M. de Berg, H. Haverkort, S. Thite, and L. Toma. Star-quadtrees and guard-quadtrees: I/O-efficient indexes for fat triangulations and low-density planar subdivisions. Comput. Geom. Theory Appl., 43:493-513, July 2010. Google Scholar
  8. P. B. Callahan and S. R. Kosaraju. A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields. J. Assoc. Comput. Mach., 42:67-90, 1995. Google Scholar
  9. P. Carmi, S. Dolev, S. Har-Peled, M. J. Katz, and M. Segal. Geographic quorum systems approximations. Algorithmica, 41(4):233-244, 2005. Google Scholar
  10. K. L. Clarkson. Nearest-neighbor searching and metric space dimensions. In G. Shakhnarovich, T. Darrell, and P. Indyk, editors, Nearest-Neighbor Methods for Learning and Vision: Theory and Practice, pages 15-59. MIT Press, 2006. Google Scholar
  11. S. Har-Peled. A replacement for Voronoi diagrams of near linear size. In Proc. 42nd Annual IEEE Symp. Found. Comput. Sci., pages 94-103, 2001. Google Scholar
  12. S. Har-Peled. Geometric Approximation Algorithms, volume 173 of Mathematical Surveys and Monographs. Amer. Math. Soc., 2011. Google Scholar
  13. S. Har-Peled, P. Indyk, and R. Motwani. Approximate nearest neighbors: Towards removing the curse of dimensionality. Theory Comput., 8:321-350, 2012. Special issue in honor of Rajeev Motwani. Google Scholar
  14. S. Har-Peled and N. Kumar. Down the rabbit hole: Robust proximity search in sublinear space. In Proc. 53rd Annual IEEE Symp. Found. Comput. Sci., pages 430-439, 2012. Google Scholar
  15. S. Har-Peled and N. Kumar. Approximating minimization diagrams and generalized proximity search. In Proc. 54th Annual IEEE Symp. Found. Comput. Sci., pages 717-726, 2013. Google Scholar
  16. S. Har-Peled and N. Kumar. Robust proximity search for balls using sublinear space. CoRR, abs/1401.1472, 2014. Google Scholar
  17. P. Indyk and R. Motwani. Approximate nearest neighbors: Towards removing the curse of dimensionality. In Proc. 30th Annual ACM Symp. Theory Comput., pages 604-613, 1998. Google Scholar
  18. G. Shakhnarovich, T. Darrell, and P. Indyk. Nearest-Neighbor Methods in Learning and Vision: Theory and Practice (Neural Information Processing). The MIT Press, 2006. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact