Skip to main content
SpringerLink
Log in

Orthogonal Range Searching on Discrete Grids

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

Years and Authors of Summarized Original Work

  • 1988; Chazelle

  • 2000; Alstrup, Brodal, Rauhe

  • 2004; JaJá, Mortensen, Shi

  • 2007; PÇŽtraÅŸcu

  • 2009; Karpinski, Nekrich

  • 2011; Chan, Larsen, PÇŽtraÅŸcu

  • 2013; Chan

Problem Definition

Let S be a set of nd-dimensional points. In the orthogonal range searching problem we keep S in a data structure, so that for an arbitrary query rectangle Q = [a1, b1] ×⋯ × [a d , b d ] information about points in Q ∩ Scan be found. Range searching is a fundamental computational geometry problem with numerous applications in data bases, text indexing, string processing, and network analysis. In computational geometry it is frequently assumed that point coordinates are real and the data structure works in the real RAM model. In a vast majority of practical situations we can, however, make a stronger assumption that point coordinates are discrete values. This scenario is captured by the word RAM model of computation: all coordinates are integers that fit into a machine word...

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 1,599.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 1,999.99
Price excludes VAT (USA)
  • Durable hardcover 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

Recommended Reading

  1. Alstrup S, Brodal G. S., Rauhe T (2000) New data structures for orthogonal range searching. In: Proceedings of the 41st annual symposium on foundations of computer science (FOCS 2000), Redondo Beach, pp 198–207

    Google Scholar 

  2. Beame P, Fich F. E. (2002) Optimal bounds for the predecessor problem and related problems. J Comput Syst Sci 65(1):38–72

    Article  MathSciNet  MATH  Google Scholar 

  3. Bentley J. L. (1980) Multi- dimensional divide-and-conquer. Commun ACM 23(4):214–229

    Article  MathSciNet  MATH  Google Scholar 

  4. Chan T. M. (2013) Persistent predecessor search and orthogonal point location on the word RAM. ACM Trans Algorithms 9(3):22

    Article  MathSciNet  MATH  Google Scholar 

  5. Chan T. M., Wilkinson B. T. (2013) Adaptive and approximate orthogonal range counting. In: Proceedings of the 24th annual ACM-SIAM symposium on discrete algorithms (SODA 2013), New Orleans, pp 241–251

    Google Scholar 

  6. Chan T. M., Larsen K. G., Pǎtraşcu M (2011) Orthogonal range searching on the RAM, revisited. In: Proceedings of the 27th SoCG, Paris, pp 1–10

    Google Scholar 

  7. Chazelle B (1988) A functional approach to data structures and its use in multi-dimensional searching. SIAM J Comput 17(3):427–462

    Article  MathSciNet  MATH  Google Scholar 

  8. Gabow H. N., Bentley J. L., Tarjan RE (1984) Scaling and related techniques for geometry problems. In: Proceedings of the 16th annual ACM symposium on theory of computing (STOC 84), Washington, DC, pp 135–143

    Chapter  Google Scholar 

  9. He M, Munro J. I. (2014) Space-efficient data structures for dynamic orthogonal range counting. Comput Geom 47(2):268–281

    Article  MathSciNet  MATH  Google Scholar 

  10. JáJá J, Mortensen C. W., Shi Q (2004) Space-efficient and fast algorithms for multi-dimensional dominance reporting and counting. In: Proceedings of the 15th international symposium on algorithms and computation (ISAAC 2004), HongKong, pp 558–568

    Google Scholar 

  11. Karpinski M, Nekrich Y (2009) Space-efficient multi-dimensional range reporting. In: Proceedings of the 15th annual international conference on computing and combinatorics (COCOON 2009), Niagara Falls, pp 215–224

    Google Scholar 

  12. Miltersen P. B., Nisan N, Safra S, Wigderson A (1998) On data structures and asymmetric communication complexity. J Comput Syst Sci 57(1):37–49

    Article  MathSciNet  MATH  Google Scholar 

  13. Nekrich Y (2009) Data structures for approximate orthogonal range counting. In: Proceedings of the 20th international symposium on algorithms and computation (ISAAC 2009), Honolulu, pp 183–192

    Google Scholar 

  14. Nekrich Y (2009) Orthogonal range searching in linear and almost-linear space. Comput Geom 42(4):342–351

    Article  MathSciNet  MATH  Google Scholar 

  15. Nekrich Y (2014) Efficient range searching for categorical and plain data. ACM Trans Database Syst 39(1):9

    Article  MathSciNet  MATH  Google Scholar 

  16. Nekrich Y, Navarro G (2012) Sorted range reporting. In: Proceedings of the 13th Scandinavian symposium and workshops on algorithm theory (SWAT 2012), Helsinki, pp 271–282

    Google Scholar 

  17. Overmars M. H. (1988) Efficient data structures for range searching on a grid. J Algorithms 9(2):254–275

    Article  MathSciNet  MATH  Google Scholar 

  18. Pǎtraşcu M (2007) Lower bounds for 2-dimensional range counting. In: Proceedings of the 39th annual ACM symposium on theory of computing (STOC 2007), San Diego, pp 40–46

    Google Scholar 

  19. Pǎtraşcu M (2010) Towards polynomial lower bounds for dynamic problems. In: Proceedings of the 42nd ACM symposium on theory of computing (STOC 2010), Cambridge, pp 603–610

    Google Scholar 

  20. Pǎtraşcu M, Thorup M (2006) Time-space trade-offs for predecessor search. In: Proceedings of the 38th annual ACM symposium on theory of computing (STOC 2006), Seattle, pp 232–240

    Google Scholar 

  21. van Emde Boas P, Kaas R, Zijlstra E (1977) Design and implementation of an efficient priority queue. Math Syst Theory 10:99–127

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhou G (2013) Sorted range reporting revisited. ArXiv e-prints 12044509 1308.3326

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Yakov Nekrich

Authors
  1. Yakov Nekrich
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yakov Nekrich .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this entry

Cite this entry

Nekrich, Y. (2016). Orthogonal Range Searching on Discrete Grids. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_631

Download citation

Publish with us

Policies and ethics

Search

Navigation