We develop a new perspective on trees, that enables us to distinguish and analyse many different subclasses of known classes of (height-)balanced search trees in a uniform manner. The approach shows that a great many different local constraints, including an arbitrary degree of density, can be enforced on everyday balanced search tree models, without losing the O(log n) bound on the time for insertions, deletions and finds. The theory extends known concepts from the study of B-trees.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Adel'son-Vel'skii, G.M., Landis, E.M.: An information organisation algorithm. Doklady Akad. Nauk SSSR 146 (1962) 263–266, transl. Soviet Math. Dokl. 3, 1259–1262 (1962)
Bayer, R.: Symmetric binary B-trees: data structure and maintenance algorithms. Acta Informat. 1, 290–306 (1972)
Bayer, R., McCreight, E.M.: Organisation and maintenance of large ordered indexes. Acta Informat. 1, 173–189 (1972)
Culik II, K., Ottmann, Th., Wood, D.: Dense multiway trees. ACM Trans. Database Syst. 6, 486–512 (1981)
Guibas, L.J., Sedgewick, R.: A dichromatic framework for balanced trees. Proc. 19th Annual IEEE Symp. on Foundations of Computer Science, Ann. Arbor, Oct. 16–18, pp. 8–21, 1978
Knuth, D.E.: The art of computer programming, vol. 3: sorting and searching. Addison-Wesley Publ. Comp., Reading, MA, 1973
Kosaraju, S.R.: Insertion and deletion in one-sided height-balanced trees. C. ACM 21, 226–227 (1978)
Olivié, H.: A study of balanced binary trees and balanced one-two trees. Ph.D. Thesis, Dept. of Mathematics, University of Antwerp (UIA), Antwerp, 1980
Ottmann, Th., Wood, D.: Deletion in one-sided height-balanced search trees. Int. J. Comput. Math. 6, 265–271 (1978)
Zweben, S.H., McDonald, M.A.: An optimal method for deletion in one-sided height-balanced trees. C. ACM 21, 441–444 (1978)
A preliminary version of this paper was presented at the meeting on “Effiziente Algorithmen und Datenstrukturen”, Oberwolfach, Feb. 2–6, 1981
The work of this author is supported by the Netherlands Organization for the Advancement of Pure Research (ZWO)
About this article
Cite this article
van Leeuwen, J., Overmars, M.H. Stratified balanced search trees. Acta Informatica 18, 345–359 (1983). https://doi.org/10.1007/BF00289574
- Information System
- Operating System
- Data Structure
- Communication Network
- Information Theory