Skip to main content
SpringerLink
Log in
Book cover

International Computing and Combinatorics Conference

COCOON 2016: Computing and Combinatorics pp 131–142Cite as

Metric 1-Median Selection: Query Complexity vs. Approximation Ratio

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9797))

Abstract

Consider the problem of finding a point in a metric space \((\{1,2,\ldots ,n\},d)\) with the minimum average distance to other points. We show that this problem has no deterministic \(o(n^{1+1/(h-1)})\)-query \((2h-\epsilon )\)-approximation algorithms for any constants \(h\in \mathbb {Z}^+\setminus \{1\}\) and \(\epsilon >0\).

C.-L. Chang—Supported in part by the Ministry of Science and Technology of Taiwan under grant 103-2221-E-155-026-MY2.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Arya, V., Garg, N., Khandekar, R., Meyerson, A., Munagala, K., Pandit, V.: Local search heuristics for \(k\)-median and facility location problems. SIAM J. Comput. 33(3), 544–562 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chang, C.-L.: A deterministic sublinear-time nonadaptive algorithm for metric \(1\)-median selection. To appear in Theoretical Computer Science

    Google Scholar 

  3. Chang, C.-L.: Some results on approximate \(1\)-median selection in metric spaces. Theor. Comput. Sci. 426, 1–12 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chang, C.-L.: Deterministic sublinear-time approximations for metric \(1\)-median selection. Inf. Process. Lett. 113(8), 288–292 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chang, C.-L.: A lower bound for metric \(1\)-median selection. Technical report. arXiv:1401.2195 (2014)

  6. Chen, K.: On coresets for \(k\)-median and \(k\)-means clustering in metric and Euclidean spaces and their applications. SIAM J. Comput. 39(3), 923–947 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Guha, S., Meyerson, A., Mishra, N., Motwani, R., O’Callaghan, L.: Clustering data streams: theory and practice. IEEE Trans. Knowl. Data Eng. 15(3), 515–528 (2003)

    Article  Google Scholar 

  8. Indyk, P.: Sublinear time algorithms for metric space problems. In: Proceedings of the 31st Annual ACM Symposium on Theory of Computing, pp. 428–434 (1999)

    Google Scholar 

  9. Indyk, P.: High-Dimensional Computational Geometry. Ph.D. thesis, Stanford University (2000)

    Google Scholar 

  10. Jaiswal, R., Kumar, A., Sen, S.: A simple \({D}^2\)-sampling based PTAS for \(k\)-means and other clustering problems. In: Proceedings of the 18th Annual International Conference on Computing and Combinatorics, pp. 13–24 (2012)

    Google Scholar 

  11. Kumar, A., Sabharwal, Y., Sen, S.: Linear-time approximation schemes for clustering problems in any dimensions. J. ACM 57(2), 5 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mettu, R.R., Plaxton, C.G.: Optimal time bounds for approximate clustering. Mach. Learn. 56(1–3), 35–60 (2004)

    Article  MATH  Google Scholar 

  13. Wu, B.-Y.: On approximating metric \(1\)-median in sublinear time. Inf. Process. Lett. 114(4), 163–166 (2014)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Yuan Ze University, Taoyuan, Taiwan

    Ching-Lueh Chang

Authors
  1. Ching-Lueh Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ching-Lueh Chang .

Editor information

Editors and Affiliations

  1. Virginia Commonwealth Univ , Richmond, Virginia, USA

    Thang N. Dinh

  2. University of Florida , Gainesville, Alabama, USA

    My T. Thai

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Chang, CL. (2016). Metric 1-Median Selection: Query Complexity vs. Approximation Ratio. In: Dinh, T., Thai, M. (eds) Computing and Combinatorics . COCOON 2016. Lecture Notes in Computer Science(), vol 9797. Springer, Cham. https://doi.org/10.1007/978-3-319-42634-1_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-42634-1_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42633-4

  • Online ISBN: 978-3-319-42634-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation