Thresholds and Optimal Binary Comparison Search Trees

Extended Abstract
  • Richard Anderson
  • Sampath Kannan
  • Howard Karloff
  • Richard E. Ladner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2245)


We present an O(n 4)-time algorithm for the following problem: Given a set of items with known access frequencies, find the optimal binary search tree under the realistic assumption that each comparison can only result in a two-way decision: either an equality comparison or a less-than comparison. This improves the best known result of O(n 5) time, which is based on split tree algorithms. Our algorithm relies on establishing thresholds on the frequency of an item that can occur as an equality comparison at the root of an optimal tree.


Side Branch Main Branch Maximum Probability Optimal Cost Binary Search Tree 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P.J. Bayer. Improved Bounds on the Cost of Optimaland Balanced Binary Search Trees. M.Sc. Thesis, MIT, MIT/LCS/TM-69, 1975.Google Scholar
  2. 2.
    C. Chambers and W. Chen. Efficient Multiple and Predicate Dispatching. Proceedings of the 1999 ACM Conference on Object-Oriented Programming Languages, Systems, and Applications (OOPSLA’ 99), November, 1999.Google Scholar
  3. 3.
    R.G. Gallager. Information Theory and Reliable Communication. Wiley, New York, 1968.zbMATHGoogle Scholar
  4. 4.
    A.M. Garsia and M.L. Wachs. A New Algorithm for Minimum Cost Binary Trees. SIAM Journal on Computing, Vol. 6, pp. 622–242, 1977.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    J.H. Hester, D.S. Hirschberg, S.-H.S. Huang, and C.K. Wong. Faster Construction of OptimalBinary Split Trees. Journal of Algorithms, Vol. 7, pp. 412–424, 1986.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    T.C. Hu and A.C. Tucker. Optimal Computer-Search Trees, and Variable Length Alphabetic Codes. SIAM Journal on Applied Mathematics, Vol. 21, pp. 514–532, 1971.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    S.-H.S. Huang and C.K. Wong. Optimal Binary Split Trees. Journal of Algorithms, Vol. 5, pp. 69–79, 1984.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    D.A. Huffman. A Method for the Construction of Minimum Redundancy Codes. Proc. Institute of Radio Engineers, Vol. 40, pp. 1098–1101, 1952.Google Scholar
  9. 9.
    D.E. Knuth. The Art of Computer Programming: Volume 3, Second Edition, Sorting and Searching. Addison-Wesley, Reading, Massachusetts, 1998.Google Scholar
  10. 10.
    K. Mehlhorn. A Best Possible Bound for the Weighted Path Length of Binary Search Trees. SIAM Journal on Computing, Vol. 6, pp. 235–239, 1977.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Y. Perl. Optimum Split Trees. Journal of Algorithms, Vol. 5, pp. 367–374, 1984.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    B.A. Sheil. Median Split Trees: A Fast Lookup Technique for Frequently Occurring Keys. Communications of the ACM, Vol. 21, pp. 947–958, 1978.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    D. Spuler. Optimal Search Trees Using Two-Way Key Comparisons. Acta Informatica, Vol. 32, pp. 729–740, 1994.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Richard Anderson
    • 1
  • Sampath Kannan
    • 2
  • Howard Karloff
    • 3
    • 5
  • Richard E. Ladner
    • 4
  1. 1.Department of Computer Science and EngineeringUniversity of WashingtonSeattle
  2. 2.AT&T Labs-Research and Department of CISUniversity of PennsylvaniaPhiladelphia
  3. 3.AT&T Labs-ResearchFlorham Park
  4. 4.Department of Computer Science and EngineeringUniversity of WashingtonSeattle
  5. 5.College of Computing, Georgia Institute of TechnologyAtlanta

Personalised recommendations