Best possible bounds on the weighted path length of optimum binary search trees

  • Kurt Mehlhorn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 33)


We derive upper and lower bounds for the weighted path length Popt of optimum binary search trees. In particular, 1/log3 H≤Popt≤2+H where H is the entropy of the frequency distribution. We also present an approximation algorithm which constructs nearly optimal trees.


Approximation Algorithm Actual Parameter Internal Node Interior Node Algorithm Construct 


  1. 1.
    E.N. Gilbert and E.F. Moore: Bell System Techn. Journal 38 (1959), 933–968.Google Scholar
  2. 2.
    T.C. Hu and K.C. Tan: Least Upper Bound on the Cost of Optimum Binary Search Trees, Acta Informatica, 1, 307–310 (1972).Google Scholar
  3. 3.
    T.C. Hu and A.C. Tucker: Optimal Computer Search Trees and variable length alphabetic codes, Siam J. Applied Math. 21, 514–532, (1971).Google Scholar
  4. 4.
    T. Kameda and K. Weihrauch: Einführung in die Kodierungstheorie, B I Skripten zur Informatik, Vol. 7.Google Scholar
  5. 5.
    D.E. Knuth: Optimum Binary Search Trees, Acta Informatica, 1, 14–25, 1971.Google Scholar
  6. 6.
    D.E. Knuth: The Art of Computer Programming, Vol. 3.Google Scholar
  7. 7.
    K. Mehlhorn: Nearly Optimum Binary Search Trees, Preprint, Fachbereich 10, Universität des Saarlandes, 1974.Google Scholar
  8. 8.
    C.P. Schnorr: Two Algorithms for Nearly Optimal Binary Search Trees, Preprint, Fachbereich Mathematik, Universität Frankfurt, 1974.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • Kurt Mehlhorn
    • 1
  1. 1.Fachbereich 1o Angewandte Mathematik und InformatikUniversität des SaarlandesSaarbrücken

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