Skip to main content
SpringerLink
Log in

Dynamic Range Selection in Linear Space

  • Conference paper
Algorithms and Computation (ISAAC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7074))

Included in the following conference series:

Abstract

Given a set S of n points in the plane, we consider the problem of answering range selection queries on S: that is, given an arbitrary x-range Q and an integer k > 0, return the k-th smallest y-coordinate from the set of points that have x-coordinates in Q. We present a linear space data structure that maintains a dynamic set of n points in the plane with real coordinates, and supports range selection queries in \(O((\lg n / \lg \lg n)^2)\) time, as well as insertions and deletions in \(O((\lg n / \lg \lg n)^2)\) amortized time. The space usage of this data structure is an \(\Theta(\lg n / \lg \lg n)\) factor improvement over the previous best result, while maintaining asymptotically matching query and update times. We also present a succinct data structure that supports range selection queries on a dynamic array of n values drawn from a bounded universe.

This work was supported by NSERC and the Canada Research Chairs Program.

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. Alstrup, S., Husfeldt, T., Rauhe, T.: Marked ancestor problems. In: Proc. 39th Annual Symposium on Foundations of Computer Science, pp. 534–543. IEEE (1998)

    Google Scholar 

  2. Arge, L., Vitter, J.S.: Optimal external memory interval management. SIAM J. Comput. 32(6), 1488–1508 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bose, P., Kranakis, E., Morin, P., Tang, Y.: Approximate Range Mode and Range Median Queries. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 377–388. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Brodal, G., Jørgensen, A.: Data Structures for Range Median Queries. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 822–831. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  5. Brodal, G., Gfeller, B., Jorgensen, A., Sanders, P.: Towards optimal range medians. Theoretical Computer Science (2010)

    Google Scholar 

  6. Cormen, T.H., Stein, C., Rivest, R.L., Leiserson, C.E.: Introduction to Algorithms, 2nd edn. McGraw-Hill Higher Education (2001)

    Google Scholar 

  7. Gagie, T., Puglisi, S.J., Turpin, A.: Range Quantile Queries: Another Virtue of Wavelet Trees. In: Karlgren, J., Tarhio, J., Hyyrö, H. (eds.) SPIRE 2009. LNCS, vol. 5721, pp. 1–6. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. Gfeller, B., Sanders, P.: Towards Optimal Range Medians. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5555, pp. 475–486. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  9. Gil, J., Werman, M.: Computing 2-d min, median, and max filters. IEEE Transactions on Pattern Analysis and Machine Intelligence 15(5), 504–507 (1993)

    Article  Google Scholar 

  10. Har-Peled, S., Muthukrishnan, S.: Range Medians. In: Halperin, D., Mehlhorn, K. (eds.) ESA 2008. LNCS, vol. 5193, pp. 503–514. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. He, M., Munro, J.I.: Succinct Representations of Dynamic Strings. In: Chavez, E., Lonardi, S. (eds.) SPIRE 2010. LNCS, vol. 6393, pp. 334–346. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  12. He, M., Munro, J.I.: Space Efficient Data Structures for Dynamic Orthogonal Range Counting. In: Dehne, F., Iacono, J., Sack, J.-R. (eds.) WADS 2011. LNCS, vol. 6844, pp. 500–511. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  13. Jacobson, G.: Space-efficient static trees and graphs. In: Proc. SFCS, pp. 549–554 (1989)

    Google Scholar 

  14. Jørgensen, A., Larsen, K.: Range selection and median: Tight cell probe lower bounds and adaptive data structures. In: Proc. SODA (2011)

    Google Scholar 

  15. Krizanc, D., Morin, P., Smid, M.: Range mode and range median queries on lists and trees. Nordic Journal of Computing 12, 1–17 (2005)

    MathSciNet  MATH  Google Scholar 

  16. Larsen, K.: The cell probe complexity of dynamic range counting. Arxiv preprint arXiv:1105.5933 (2011)

    Google Scholar 

  17. Pǎtraşcu, M.: Lower bounds for 2-dimensional range counting. In: Proc. 39th ACM Symposium on Theory of Computing (STOC), pp. 40–46 (2007)

    Google Scholar 

  18. Petersen, H.: Improved Bounds for Range Mode and Range Median Queries. In: Geffert, V., Karhumäki, J., Bertoni, A., Preneel, B., Návrat, P., Bieliková, M. (eds.) SOFSEM 2008. LNCS, vol. 4910, pp. 418–423. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  19. Petersen, H., Grabowski, S.: Range mode and range median queries in constant timeand sub-quadratic space. Inf. Process. Lett. 109, 225–228 (2009)

    Article  MATH  Google Scholar 

  20. Raman, R., Raman, V., Rao, S.S.: Succinct Dynamic Data Structures. In: Dehne, F., Sack, J.-R., Tamassia, R. (eds.) WADS 2001. LNCS, vol. 2125, pp. 426–437. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Computer Science, Dalhousie University, Canada

    Meng He

  2. David R. Cheriton School of Computer Science, University of Waterloo, Canada

    J. Ian Munro & Patrick K. Nicholson

Authors
  1. Meng He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Ian Munro
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Patrick K. Nicholson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Chuo University, Kasuga, Bunkyo-ku, 112-8551, Tokyo, Japan

    Takao Asano

  2. Gunma University, 1-5-1 Tenjin-Cho, 376-8515, Kiryu-Shi, Japan

    Shin-ichi Nakano

  3. Japan Advanced Institute of Science and Technology, 1-1 Asahidai, 923-1292, Nomi, Ishikawa, Japan

    Yoshio Okamoto

  4. Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, 152-8552, Tokyo, Japan

    Osamu Watanabe

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

He, M., Munro, J.I., Nicholson, P.K. (2011). Dynamic Range Selection in Linear Space. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-25591-5_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25590-8

  • Online ISBN: 978-3-642-25591-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation