Skip to main content
SpringerLink
Log in

Computing k-center over Streaming Data for Small k

  • Conference paper
Algorithms and Computation (ISAAC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7676))

Included in the following conference series:

  • 1487 Accesses

Abstract

The Euclidean k-center problem is to compute k congruent balls covering a given set of points in ℝd such that the radius is minimized. We consider the k-center problem in ℝd for k = 2,3 in a single-pass streaming model, where data is allowed to be examined once and only a small amount of information can be stored in a device. We present two approximation algorithms whose space complexity does not depend on the size of the input data. The first algorithm guarantees a (2 + ε)-factor using O(d/ε) space in arbitrary dimensions, and the second algorithm guarantees a (1 + ε)-factor using O(1/ε d) space in constant dimensions. The same algorithms can be used to compute a k-center under any L p metric for k = 2,3.

This research is supported by the NRF grant 2011-0030044 (SRC-GAIA) funded by the government of Korea.

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

Access this chapter

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 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agarwal, P.K., Har-Peled, S., Varadarajan, K.R.: Approximating extent measures of points. Journal of the ACM 51(4), 606–635 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Agarwal, P.K., Procopiuc, C.M.: Exact and approximation algorithms for clustering. Algorithmica 33, 201–226 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. Agarwal, P.K., Sharathkumar, R.: Streaming algorithms for extent problems in high dimensions. In: Proc. of the 21st ACM-SIAM Sympos. Discrete Algorithms, pp. 1481–1489 (2010)

    Google Scholar 

  4. Aggarwal, C.C.: Data streams: models and algorithms. Springer (2007)

    Google Scholar 

  5. Bern, M., Eppstein, D.: Approximation algorithms for geometric problems. In: Approximation Algorithms for NP-Hard Problems. PWS Publishing Co. (1996)

    Google Scholar 

  6. Chan, T.M.: More planar two-center algorithms. Computational Geometry 13(3), 189–198 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  7. Chan, T.M.: Faster core-set constructions and data-stream algorithms in fixed dimensions. Computational Geometry 35, 20–35 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chan, T.M., Pathak, V.: Streaming and Dynamic Algorithms for Minimum Enclosing Balls in High Dimensions. In: Dehne, F., Iacono, J., Sack, J.-R. (eds.) WADS 2011. LNCS, vol. 6844, pp. 195–206. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  9. Charikar, M., Chekuri, C., Feder, T., Motwani, R.: Incremental clustering and dynamic information retrieval. SIAM J. Comput. 33(6), 1417–1440 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chazelle, B., Matoušek, J.: On linear-time deterministic algorithms for optimization problems in fixed dimension. Journal of Algorithms 21, 579–597 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  11. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)

    MATH  Google Scholar 

  12. Guha, S.: Tight results for clustering and summarizing data streams. In: Proc. of the 12th Int. Conf. on Database Theory, pp. 268–275. ACM (2009)

    Google Scholar 

  13. Hershberger, J., Suri, S.: Adaptive sampling for geometric problems over data streams. Computational Geometry 39(3), 191–208 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zarrabi-Zadeh, H.: Core-preserving algorithms. In: Proc. of 20th Canadian Conf. on Comput. Geom. (CCCG), pp. 159–162 (2008)

    Google Scholar 

  15. McCutchen, R.M., Khuller, S.: Streaming Algorithms for k-Center Clustering with Outliers and with Anonymity. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds.) APPROX and RANDOM 2008. LNCS, vol. 5171, pp. 165–178. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  16. Megiddo, M.: On the complexity of some geometric problems in unbounded dimension. J. Symbolic Comput. 10, 327–334 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  17. Megiddo, M., Supowit, K.J.: On the complexity of some common geometric location problems. SIAM J. Comput. 13(1), 182–196 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  18. Poon, C.K., Zhu, B.: Streaming with Minimum Space: An Algorithm for Covering by Two Congruent Balls. In: Lin, G. (ed.) COCOA 2012. LNCS, vol. 7402, pp. 269–280. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  19. Zarrabi-Zadeh, H.: An almost space-optimal streaming algorithm for coresets in fixed dimensions. Algorithmica 60, 46–59 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  20. Zarrabi-Zadeh, H., Chan, T.M.: A simple streaming algorithm for minimum enclosing balls. In: Proc. of 18th CCCG, pp. 139–142 (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Pohang University of Science and Technology, Korea

    Hee-Kap Ahn, Hyo-Sil Kim, Sang-Sub Kim & Wanbin Son

Authors
  1. Hee-Kap Ahn
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hyo-Sil Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sang-Sub Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wanbin Son
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Information Engineering, National Taiwan University, 1 Roosevelt Road, Section 4, 106, Taipei, Taiwan

    Kun-Mao Chao

  2. Institute of Information Science, Academia Sinica, 128 Academia Road, Section 2, 115, Taipei, Taiwan

    Tsan-sheng Hsu

  3. Department of Computer Science and Engineering, National Chung Hsing University, 250 Kuo Kuang Road, 402, Taichung, Taiwan

    Der-Tsai Lee

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ahn, HK., Kim, HS., Kim, SS., Son, W. (2012). Computing k-center over Streaming Data for Small k . In: Chao, KM., Hsu, Ts., Lee, DT. (eds) Algorithms and Computation. ISAAC 2012. Lecture Notes in Computer Science, vol 7676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35261-4_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-35261-4_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35260-7

  • Online ISBN: 978-3-642-35261-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation