Abstract
We analyze the performance of search trees built under a variety of insertion heuristics. The main results are a method to obtain asymptotic expressions for the moments of the distribution of the search time, and a proof that this distribution is asymptotically normal.
Similar content being viewed by others
References
Abramowitz, M., Stegun, I.A. (eds.): Handbook of mathematical functions. New York: Dover 1968
Comtet, L.: Advanced combinatorics. Dordrecht: Reidel 1974
Cunto, W., Gascon, J.L.: Improving time and space efficiency in generalized binary search trees. Acta Inf.24, 583–594 (1987)
Cunto, W., Gonnet, G.H., Munro, J.I., Poblete, P.V.: Fringe analysis for extquick: an in situ distributive external sorting algorithm. Inf. Comput.92(2), 141–160 (1991)
Gantmacher, F.R.: The theory of matrices, vol. 1. Broomall, PA: Chelsea 1959
Gantmacher, F.R.: Applications of the theory of matrices. New York: Interscience 1959
Gnedenko, B.V., Kolmogorov, A.N.: Limit distributions for sums of independent random variables. Reading, MA: Addison-Wesley 1954
Goncharov, V.: On the field of combinatory analysis. Izv. Akad. Nauk SSSR Ser. Math.8 (1944)
Gonnet, G.H., Baeza-Yates R.: Handbook of algorithms and data structures, 2nd edn. Reading, MA: Addison-Wesley 1991
Greene, D.H., Knuth, D.E.: Mathematics for the analysis of algorithms. Boston: Birkhäuser 1982
Knott, G.D.: Deletions in binary storage trees. Report STAN-CS-75-491, Stanford University, May 1975
Knuth, D.E.: The art of computer programming, vol. 1: fundamental algorithms. Reading MA: Addison-Wesley 1973
Knuth, D.E.: The art of computer programming, vol. 3: sorting and searching. Reading MA: Addison-Wesley 1973
Munro, J.I., Poblete, P.V.: Fault tolerance and storage reduction in binary search trees. Inf. Control62(3), 210–219 (1984)
Poblete, P.V., Munro, J.I.: The analysis of a fringe heuristic for binary search trees. J. Algorithms6, 336–350 (1985)
Sedgewick, R.: Quicksort. Report STAN-CS-75-492, Stanford University, 1975
Seneta, E.: Non-negative matrices and Markov chains. (Springer Series Statistics) Berlin Heidelberg New York: Springer 1981
Wilkinson, J.H.: The algebraic eigenvalue problem. Oxford: Oxford University Press 1965
Author information
Authors and Affiliations
Additional information
This work was supported by National Science and Engineering Research Council of Canada grant A-8237, and by FONDECYT (Chile) grant 91-1252.
Rights and permissions
About this article
Cite this article
Poblete, P.V. The analysis of heuristics for search trees. Acta Informatica 30, 233–248 (1993). https://doi.org/10.1007/BF01179372
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01179372