Advertisement

Searchability in merging and implicit data structures

  • J. Ian Munro
  • Patricio V. Poblete
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 154)

Abstract

We introduce the notion of searchability as a property of an in place merging algorithm. It is shown that a pair of sorted arrays can be merged in place in linear time so that a logarithmic time search may be performed at any point during the process. This method is applied to devise an implicit data structure which can support searches in 0(log2 n) time and insertions in 0(log n) time.

Keywords

Binary Search Internal Move Binary Search Tree Merging Algorithm Average Search 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Bentley, J.L., D. Detig, L. Guibas and J.B. Saxe: An Optimal Data Structure for Minimal-Storage Dynamic Member Searching, Carnegie-Mellon University, 1978.Google Scholar
  2. [2]
    Bentley, J.L. and J.B. Saxe: Decomposable Searching Problems I. Static-to-Dynamic Transformation, Journal of Algorithms, 1, 4 (Dec. 1980), 301–358.Google Scholar
  3. [3]
    Borodin, A.B., L.J. Guibas, N.A. Lynch and A.C. Yao: Efficient Searching Using Partial Ordering, IPL (12,2) April 1981, 71–75.Google Scholar
  4. [4]
    Eppinger, J.L., An Empirical Study of Insertion and Deletion in Binary Trees (Sept. 1982) unpublished manuscript.Google Scholar
  5. [5]
    Frederickson, G.N.: Implicit Data Structures with Fast Update, 21st Annual Symposium on Foundations of Computer Science, 1980, 255–259.Google Scholar
  6. [6]
    Horvath, E.C.: Stable Sorting in Asymptotically Optimal Time and Extra Space, Journal of the ACM, 25, 2 (April 1978), 177–199.Google Scholar
  7. [7]
    Hwang, F.K. and S. Lin: A Simple Algorithm for Merging Two Disjoint Linearly Ordered Sets, SIAM Journal on Computing, 1, 1 (March 1972), 31–39.Google Scholar
  8. [8]
    Jonassen, A.T. and D.E. Knuth: A Trivial Algorithm Whose Analysis Isn't, Journal of Computer and System Sciences, 16, 3 (June 1978), 301–322.Google Scholar
  9. [9]
    Knott, G.D.: Deletion in Binary Storage Trees, Dept. of Computer Science, Stanford University, Rep. STAN-CS-75-491, May 1975.Google Scholar
  10. [10]
    Knuth, D.E.: The Art of Computer Programming, Vol. 3: Sorting and Searching, Addison-Wesley, Reading, MA., 1973.Google Scholar
  11. [11]
    Knuth, D.E.: Deletions that Preserve Randomness, IEEE Transactions on Software Engineering, SE-3, 5 (Sept. 1977), 351–359.Google Scholar
  12. [12]
    Kronrod, M.A.: An Optimal Ordering Algorithm Without a Field of Operation, Dok. Akad. Nauk SSSR, 186 (1969), 1256–1258.Google Scholar
  13. [13]
    Munro, J.I. and H. Suwanda: Implicit Data Structure for Fast Search and Update, Journal of Computer and System Sciences, 21 2 (Oct. 1980), 236–250.Google Scholar
  14. [14]
    Trabb Pardo, L.: Stable Sorting and Merging with Optimal Space and Time Bounds, SIAM Journal on Computing, 6, 2 (June 1977), 351–372.Google Scholar
  15. [15]
    Wong, J.K.: Some Simple In-place merging Algorithms, BIT 21 (1981), 157–166.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • J. Ian Munro
    • 1
  • Patricio V. Poblete
    • 2
  1. 1.Data Structuring Group Department of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Computer Science DivisionUniversity of ChileSantiagoChile

Personalised recommendations