On the mean weight balance factor of binary trees
A new performance measure for binary trees, called the mean weight balance factor (MWBF), is introduced. For any binary tree T, 0<MWBF (T)≤1. Very unbalanced trees have MWBF close to 0, while complete binary trees have MWBF close to 1. The expected MWBF of a binary tree under random insertions is derived. It is shown that an AVL tree has an MWBF of atleast 0.73. Bounds are also obtained on the expected MWBF of an AVL tree under random insertions.
KeywordsBinary Tree External Node Successful Search Random Insertion Complete Binary Tree
Unable to display preview. Download preview PDF.
- 1.A. Bagchi and A. K. Pal Asymptotic Normality in the Generalized Polya-Eggenberger Urn Model, With an Application to Computer Data Structures SIAM Jr. Alg. Disc. Meth., (to appear).Google Scholar
- 2.A. Bagchi and E. M. Reingold A Naturally Occurring Function Continuous Only at Irrationals American Math. Monthly, Vol. 89, No. 6, June–July 1982, pp. 411–417.Google Scholar
- 3.M. R. Brown A Partial Analysis of Random Height-Balanced Trees SIAM Jr. Comp., Vol.8, No.1, Feb. 1979, pp.33–41.Google Scholar
- 4.D. E. Knuth The Art of Computer Programming, Vol.I, Fundamental Algorithms (2nd Ed.) Addison Wesley, 1975.Google Scholar
- 5.D. E. Knuth The Art of Computer Programming, Vol.III, Sorting and Searching Addison Wesley, 1975.Google Scholar
- 6.A. K. Pal and A. Bagchi Analysis of a Simple Insertion Algorithm for 3-trees Proc. 3rd Ann. Conf. on Foundations of Software Tech. and Theo. Comp. Sc., Bangalore (India), Dec. 12–14, 1983, pp.390–417.Google Scholar
- 7.E. M. Reingold, J. Nievergelt and N. Deo Combinatorial Algorithms Prentice Hall, 1977.Google Scholar