Summary
We analyze storage utilization in random B *-trees (trees, where all data are stored in the leaf nodes). Extending a proposal of Bayer and McCreight, in case of insertion into a full node, up to m}-1 adjacent nodes are scanned for empty space. If this search is successful, entries are shifted on leaf level to gain free space for the new one; otherwise, the entries of the m nodes scanned are distributed as uniformly as possible over m}+1 nodes. Using iterative models it is shown that for large trees of high order storage utilization converges to m · ln((m}+1)/m).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bayer, R., McCreight, E.: Organization and Maintenance of Large Ordered Indexes. Acta Informat. 1, 173–189 (1972)
Bayer, R., Unterauer, K.: Prefix B-Trees. ACM Trans. Database Syst. 2, 11–26 (1977)
Comer, D.: The Ubiquitous B-Tree. Comput. Surv. 11, 121–137 (1979)
Culik, K., Ottmann, T., Wood, D.: Dense Multiway Trees. ACM Trans. Database Syst. 6, 486–512 (1981)
Effelsberg, W., Reuter, A.: Performance Handbook UDS V2 BS 1000.Technical Report (in German), Technical University of Darmstadt, Department of Computer Science, 1979
Klopprogge, M.R., Quitzow, K.: Space Utilization and Access Path Length in B-Trees. Informat. Syst. 5, 7–16 (1980)
Knuth, D.E.: The Art of Computer Programming. Vol. 3: Sorting and Searching, 2 nd ed., Reading, MA: Addison-Wesley, 1975
Küspert, K., Meyer-Wegener, K.: Design and Implementation of a System for Performance Prediction in UDS using Analytic Models. Master's Theses (in German), Technical University of Darmstadt, Department of Computer Science, 1980
Lomet, D.B.: Digital B-Trees. Proc. 7th Int. Conf. on VLDB, Cannes, pp. 333–344,1981
Nakamura, T., Mizoguchi, T.: An Analysis of Storage Utilization Factor in Block Split Data Structuring Scheme. Proc. 4th Int. Conf. on VLDB, Berlin, pp. 489–495, 1978
Neff, W.: Analysis of Access Time in B *-Trees. Master's Thesis (in German), Technical University of Darmstadt, Department of Computer Science, 1980
Quitzow, K.: Analysis of Space Utilization and Path Length in B-Trees. Master's Thesis (in German), University of Karlsruhe, Department of Computer Science, 1977
Rehbein, J.: Analysis of Update Operations in a Data Base System. Master's Thesis (in German), Technical University of Darmstadt, Department of Computer Science, 1979
Data Base System UDS. System and Operations, Reference Manual (BS 2000), Siemens AG, Munich, 1981
Wedekind, H.: On the Selection of Access Paths in a Data Base System. Data Base Management. Proc. IFIP Working Conference on Data Base Management. Klimbie, J.W., Koffeman, K.L., (eds.), pp. 385–397, Amsterdam: North-Holland, 1974
Yao, A.C.: On Random 2–3 Trees. Acta Informat. 9, 159–170 (1978)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Küspert, K. Storage utilization in B *-trees with a generalized overflow technique. Acta Informatica 19, 35–55 (1983). https://doi.org/10.1007/BF00263927
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00263927