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Data Structures for Range Median Queries

  • Gerth Stølting Brodal
  • Allan Grønlund Jørgensen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5878)

Abstract

In this paper we design data structures supporting range median queries, i.e. report the median element in a sub-range of an array. We consider static and dynamic data structures and batched queries. Our data structures support range selection queries, which are more general, and dominance queries (range rank). In the static case our data structure uses linear space and queries are supported in O(logn/loglogn) time. Our dynamic data structure uses O(nlogn/loglogn) space and supports queries and updates in O((logn/loglogn)2) time.

Keywords

Data Structure Binary Search Small Element Query Time Current Section 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Krizanc, D., Morin, P., Smid, M.H.M.: Range mode and range median queries on lists and trees. Nord. J. Comput. 12(1), 1–17 (2005)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Petersen, H.: Improved bounds for range mode and range median queries. In: Proc. 34th Conference on Current Trends in Theory and Practice of Computer Science, pp. 418–423 (2008)Google Scholar
  3. 3.
    Petersen, H., Grabowski, S.: Range mode and range median queries in constant time and sub-quadratic space. Inf. Process. Lett. 109(4), 225–228 (2009)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Gfeller, B., Sanders, P.: Towards optimal range medians. In: Proc. 36th International Colloquium on Automata, Languages and Programming, pp. 475–486 (2009)Google Scholar
  5. 5.
    Gagie, T., Puglisi, S.J., Turpin, A.: Range quantile queries: Another virtue of wavelet trees. In: Proc. 16th String Processing and Information Retrieval Symposium, pp. 1–6 (2009)Google Scholar
  6. 6.
    Har-Peled, S., Muthukrishnan, S.: Range medians. In: Proc. 16th Annual European Symposium on Algorithms, pp. 503–514 (2008)Google Scholar
  7. 7.
    Pǎtraşcu, M.: Lower bounds for 2-dimensional range counting. In: Proc. 39th ACM Symposium on Theory of Computing, pp. 40–46 (2007)Google Scholar
  8. 8.
    Pǎtraşcu, M.: (Data) STRUCTURES. In: Proc. 49th Annual IEEE Symposium on Foundations of Computer Science, pp. 434–443 (2008)Google Scholar
  9. 9.
    JáJá, J., Mortensen, C.W., Shi, Q.: Space-efficient and fast algorithms for multidimensional dominance reporting and counting. In: Proc. 15th International Symposium on Algorithms and Computation, pp. 558–568 (2004)Google Scholar
  10. 10.
    Nekrich, Y.: Orthogonal range searching in linear and almost-linear space. In: Proc. 10th International Workshop on Algorithms and Data Structures, pp. 15–26 (2007)Google Scholar
  11. 11.
    Alstrup, S., Husfeldt, T., Rauhe, T.: Marked ancestor problems. In: Proc. 39th Annual Symposium on Foundations of Computer Science, Washington, DC, USA, pp. 534–543. IEEE Computer Society, Los Alamitos (1998)Google Scholar
  12. 12.
    Chazelle, B., Guibas, L.J.: Fractional cascading: I. A data structuring technique. Algorithmica 1(2), 133–162 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Jacobson, G.J.: Succinct static data structures. PhD thesis. Carnegie Mellon University, Pittsburgh, PA, USA (1988)Google Scholar
  14. 14.
    van Emde Boas, P., Kaas, R., Zijlstra, E.: Design and implementation of an efficient priority queue. Mathematical Systems Theory 10, 99–127 (1977)zbMATHCrossRefGoogle Scholar
  15. 15.
    Nievergelt, J., Reingold, E.M.: Binary search trees of bounded balance. In: Proc. 4th Annual ACM symposium on Theory of computing, pp. 137–142 (1972)Google Scholar
  16. 16.
    Arge, L., Vitter, J.S.: Optimal external memory interval management. SIAM Journal on Computing 32(6), 1488–1508 (2003)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Gerth Stølting Brodal
    • 1
  • Allan Grønlund Jørgensen
    • 1
  1. 1.MADALGO, Department of Computer ScienceAarhus UniversityDenmark

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