A new algorithm for the construction of optimal B-trees

  • Peter Becker
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 824)


In this paper the construction of optimal B-trees for n keys, n key weights, and n+1 gap weights, is investigated. The best algorithms up to now have running time O(k n3 log n), where k is the order of the B-tree. These algorithms are based on dynamic programming and use step by step construction of larger trees from optimal smaller trees. We present a new algorithm, which has running time O(k nα), with α=2+log 2/log(k+1). This is a substantial improvement to the former algorithms. The improvement is achieved by applying a different dynamic programming paradigm. Instead of step by step construction from smaller subtrees a decison model is used, where the keys are placed by a sequential decision process in such a way into the tree, that the costs become optimal and the B-tree constraints are valid.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Bayer and E. M. McCreight, “Organization and Maintenance of Large Ordered Indexes,” Acta Informatica, vol. 1, pp. 173–189, 1972.CrossRefGoogle Scholar
  2. 2.
    L. Gotlieb, “Optimal Multi-Way Search Trees,” SIAM Journal of Computing, vol. 10, no. 3, pp. 422–433, 1981.Google Scholar
  3. 3.
    Shou-Hsuan Stephen Huang and Venkatraman Viswanathan, “On the Construction of Weighted Time-Optimal B-Trees,” Bit, vol. 30, pp. 207–215, 1990.Google Scholar
  4. 4.
    D. E. Knuth, “Optimum Binary Search Trees,” Acta Informatica, vol. 1, pp. 14–25, 1971.CrossRefGoogle Scholar
  5. 5.
    K. Neumann and M. Morlock, Operations Research, Hanser, Munich, 1993.Google Scholar
  6. 6.
    J. Pearl, Heuristics — Intelligent Search Strategies for Computer Problem Solving, Addison-Wesley, 1984.Google Scholar
  7. 7.
    V. K. Vaishnavi, H. P. Kriegel, and D. Wood, “Optimum Multiway Search Trees,” Acta Informatica, vol. 14, pp. 119–133, 1980.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Peter Becker
    • 1
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenGermany

Personalised recommendations