Skip to main content
SpringerLink
Log in

In-Place Algorithms for Computing (Layers of) Maxima

  • Conference paper
Algorithm Theory – SWAT 2006 (SWAT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4059))

Included in the following conference series:

Abstract

We describe space-efficient algorithms for solving problems related to finding maxima among points in two and three dimensions. Our algorithms run in optimal \(\mathcal{O}({n\log n})\) time and occupy only constant extra space in addition to the space needed for representing the input.

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. Bentley, J.L.: Multidimensional divide-and-conquer. Communications of the ACM 23(4), 214–229 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bentley, J.L., Clarkson, K.L., Levine, D.B.: Fast linear expected-time algorithms for computing maxima and convex hulls. Algorithmica 9(2), 168–183 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  3. Börzsönyi, S., Kossmann, D., Stocker, K.: The skyline operator. In: Proceedings of the 17th International Conference on Data Engineering, pp. 421–430 (2001)

    Google Scholar 

  4. Bose, P., Maheshwari, A., Morin, P., Morrison, J., Smid, M., Vahrenhold, J.: Space-efficient geometric divide-and-conquer algorithms. Computational Geometry: Theory & Applications (to appear, 2006) (accepted, November 2004)

    Google Scholar 

  5. Brönnimann, H., Chan, T.M.-Y.: Space-efficient algorithms for computing the convex hull of a simple polygonal line in linear time. Computational Geometry: Theory & Applications 34(2), 75–82 (2006)

    MATH  Google Scholar 

  6. Brönnimann, H., Chan, T.M.-Y., Chen, E.Y.: Towards in-place geometric algorithms. In: Proceedings of the 20th Annual Symposium on Computational Geometry, pp. 239–246 (2004)

    Google Scholar 

  7. Brönnimann, H., Iacono, J., Katajainen, J., Morin, P., Morrison, J., Toussaint, G.T.: Space-efficient planar convex hull algorithms. Theoretical Computer Science 321(1), 25–40 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  8. Buchsbaum, A.L., Goodrich, M.T.: Three-dimensional layers of maxima. Algorithmica 39(4), 275–286 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  9. Chen, E.Y., Chan, T.M.-Y.: A space-efficient algorithm for line segment intersection. In: Proceedings of the 15th Canadian Conference on Computational Geometry, pp. 68–71 (2003)

    Google Scholar 

  10. Dai, H.K., Zhang, X.W.: Improved linear expected-time algorithms for computing maxima. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 181–192. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  11. Floyd, R.W.: Algorithm 245: Treesort. Communications of the ACM 7(12), 701 (1964)

    Article  Google Scholar 

  12. Geffert, V., Katajainen, J., Pasanen, T.: Asymptotically efficient in-place merging. Theoretical Computer Science 237(1–2), 159–181 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  13. Kapoor, S.: Dynamic maintenance of maxima of 2-D point sets. SIAM Journal on Computing 29(6), 1858–1877 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  14. Katajainen, J., Pasanen, T.: Stable minimum space partitioning in linear time. BIT 32, 580–585 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kossmann, D., Ramsak, F., Rost, S.: Shooting stars in the sky: An online algorithm for skyline queries. In: Proceedings of the 28th International Conference on Very Large Data Bases, pp. 275–286 (2002)

    Google Scholar 

  16. Kung, H.T., Luccio, F., Preparata, F.P.: On finding the maxima of a set of vectors. Journal of the ACM 22(4), 469–476 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  17. Matoušek, J.: Computing dominances in E n. Information Processing Letters 38(5), 277–278 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  18. Munro, J.I.: An implicit data structure supporting insertion, deletion, and search in O(log2 n) time. Journal of Computer and System Sciences 33(1), 66–74 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  19. Papadias, D., Tao, Y., Fu, G., Seeger, B.: Progressive skyline computation in database systems. ACM Transactions on Database Systems 30(1), 41–82 (2005)

    Article  Google Scholar 

  20. Preparata, F.P., Shamos, M.I.: Computational Geometry. An Introduction. Springer, Heidelberg (1988)

    Google Scholar 

  21. Salowe, J.S., Steiger, W.L.: Stable unmerging in linear time and constant space. Information Processing Letters 25(3), 285–294 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  22. Tan, K.-L., Eng, P.-K., Ooi, B.C.: Efficient progressive skyline computation. In: Proceedings of the 27th International Conference on Very Large Data Bases, pp. 301–310 (2001)

    Google Scholar 

  23. Vahrenhold, J.: Line-segment intersection made in-place. In: Dehne, F., López-Ortiz, A., Sack, J.-R. (eds.) WADS 2005. LNCS, vol. 3608, pp. 146–157. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Westfälische Wilhelms-Universität Münster, 48149, Münster, Germany

    Henrik Blunck & Jan Vahrenhold

Authors
  1. Henrik Blunck
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jan Vahrenhold
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. MADALGO, Department of Computer Science, University of Aarhus, Denmark

    Lars Arge

  2. Institute of Mathematics and Computer Science, University of Latvia, Raiņa bulvāris 29, Rīga, LV-1459, Latvia

    Rusins Freivalds

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Blunck, H., Vahrenhold, J. (2006). In-Place Algorithms for Computing (Layers of) Maxima. In: Arge, L., Freivalds, R. (eds) Algorithm Theory – SWAT 2006. SWAT 2006. Lecture Notes in Computer Science, vol 4059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11785293_34

Download citation

  • DOI: https://doi.org/10.1007/11785293_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35753-7

  • Online ISBN: 978-3-540-35755-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation