Skip to main content
SpringerLink
Log in

On the correspondence between AVL trees and brother trees

Über den Zusammenhang zwischen AVL-Bäumen und Bruder-Bäumen

  • Published:
Computing Aims and scope Submit manuscript

Abstract

We discuss the relationships of the classes of height-balanced (search) trees and the classes of brother (search) trees. In particular we characterize each class of height-balanced trees in terms of the class of “corresponding” brother trees and vice versa. Secondly, we show how this characterization leads to the notion of nonstandard updating algorithms. We derive a nonstandard insertion algorithm for height-balanced search trees to illustrate the notion. Finally we consider something of the similarities and differences between the standard and nonstandard insertion algorithms for height-balanced search rees.

Zusammenfassung

Wir diskutieren die Beziehungen zwischen der Klasse der höhenbalanzierten (Such-) Bäume und der Klasse der Bruder-(Such-) Bäume. Insbesondere wird jede Klasse höhenbalanzierter Bäume durch die Klasse “entsprechender” Bruder-Bäume charakterisiert und umgekehrt. Zweitens zeigen wir, wie diese Charakterisierung zu nichtstandard Rebalanzierungs-Algorithmen führt. Wir erläutern dies am Beispiel des Einfüge-Algorithmus für höhenbalanzierte Bäume. Abschließend gehen wir auf einige Ähnlichkeiten und Unterschiede zwischen standard- und nichtstandard Einfüge-Algorithmen für höhenbalanzierte Bäume ein.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Culik II, K., Ottmann, Th., Wood, D.: Dense multiway trees. Technical Report No. 77, Institut für Angewandte Informatik und Formale Beschreibungsverfahren, Karlsruhe, 1978.

  2. Foster, C. C.: A generalization of AVL trees. Communications of the ACM16, 8, 513–517 (1973).

    Article  Google Scholar 

  3. Knuth, D.: The art of computer programming, Vol. 3, sorting and searching. Reading, Mass.: Addison-Wesley 1973.

    Google Scholar 

  4. Luccio, R., Pagli, L.: On the height of height-balanced trees. IEEE Transactions on ComputersC25, 87–90 (1976).

    Google Scholar 

  5. Melhorn, K.: Effiziente Algorithmen. Stuttgart: Teubner 1977.

    Google Scholar 

  6. Ottmann, Th., Six, H.-W.: Eine neue Klasse von ausgeglichenen Binärbäumen. Angewandte Informatik8, 395–400 (1976).

    Google Scholar 

  7. Ottmann, Th., Six, H.-W., Wood, D.: New results in balanced search trees. Applied Computer Science. München: Carl Hanser 1978.

    Google Scholar 

  8. Ottmann, Th., Six, H.-W., Wood, D.: Right brother trees. Communications of the ACM21, 9, 769–776 (1978).

    Article  Google Scholar 

  9. Ottmann, Th., Six, H.-W., Wood, D.: One-sided k-height-balanced trees. Computing (1979), to appear.

  10. Ottmann, Th., Wood, D.: 1–2 brother trees or AVL trees revisited. The Computer Journal (1979), to appear.

  11. van Leeuwen, J.: The complexity of data organization, in: Foundations of Computer Science, Part I (Apt, de Bakker, eds.). Mathematical Centre Tracts 81, Amsterdam, 37–147 (1976).

Download references

Author information

Authors and Affiliations

  1. Institut für Angewandte Informatik und Formale Beschreibungsverfahren, Universität Karlsruhe, Kollegium am Schloß, Bau IV, D-7500, Karlsruhe, Federal Republic of Germany

    Th Ottmann & H. -W. Six

  2. Unit for Computer Science, McMaster University, L8S 4K1, Hamilton, Ontario, Canada

    D. Wood

Authors
  1. Th Ottmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. -W. Six
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. Wood
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Work carried out partially under the auspices of the University of Karlsruhe and partially under a Natural Sciences and Engineering Research Council of Canada Grant No. A-7700.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ottmann, T., Six, H.W. & Wood, D. On the correspondence between AVL trees and brother trees. Computing 23, 43–54 (1979). https://doi.org/10.1007/BF02252612

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02252612

Keywords

Search

Navigation