Skip to main content

AVL-trees for localized search

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 172))

Abstract

We present a data structure based on AVL-trees which allows to perform an insertion or a deletion in time O(log d) where'd is the distance of the position searched for from the finger which points to the end of the file. Moving a finger costs O(log d). This result demonstrates the power of the oldest basic data structure, the AVL-tree. A special case of interest is an efficient implementation of searchable priority queues such that Deletemin requires only constant time.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. ADELSON-VELSKII, G.M. LANDIS, "An Algorithm for the organisation of information" (in Russian), Dokl.Ak.Nauk SSSR Vol. 146, p. 263–266 (1962)

    Google Scholar 

  2. N. BLUM and K. MEHLHORN, "On the average number of rebalancing operations in weight-balanced trees" TCS 11, p. 303–320 (1980)

    Google Scholar 

  3. M. BROWN and R. TARJAN, "Design and analysis of a data structure for representing sorted lists", SIAM J. Computing Vol 9, p. 594–614 (1980)

    Google Scholar 

  4. C.C. FOSTER, "Information storage and retrieval using AVL-trees" ACM 20th National Conference, p. 192–205 (1965)

    Google Scholar 

  5. L. GUIBAS, E. MC. CREIGHT, M. PLASS, J. ROBERTS, "A new representation of linear lists" 9th STOC, p. 49–60 (1977)

    Google Scholar 

  6. Sc. HUDDLESTON, "An efficient scheme for fast local updates in linear lists", University of California at Irvine (1981)

    Google Scholar 

  7. S. HUDDLESTON and K. MEHLHORN, "A new data structure for representing sorted lists" Acta Informatica 17, p. 157–184 (1982)

    Google Scholar 

  8. D. KNUTH, "The art of computer programming", Vol 3, Sorting and Searching. Addison Wesley Reading Mass. (1973)

    Google Scholar 

  9. S.R. KOSARAJU, "Localized search in sorted lists" 14 STOC, p. 62–69 (1981)

    Google Scholar 

  10. K. MEHLHORN, "Sorting presorted files", 4th GI-Conference on Theoretical Computer Science, Aachen LNCS Vol. 67, p. 199–219 (1979)

    Google Scholar 

  11. K. MEHLHORN and A. TSAKALIDIS, "AVL-trees, refined analysis and application to sorting presorted files", Technischer Bericht A82/05, FB 10 Universität des Saarlandes (1982)

    Google Scholar 

  12. R.E. TARJAN, private communication

    Google Scholar 

  13. A. TSAKALIDIS, "AVL-trees for localized Search", Technischer Bericht A 83/13, FB 10, Universität des Saarlandes (1983)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jan Paredaens

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Tsakalidis, A.K. (1984). AVL-trees for localized search. In: Paredaens, J. (eds) Automata, Languages and Programming. ICALP 1984. Lecture Notes in Computer Science, vol 172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13345-3_44

Download citation

  • DOI: https://doi.org/10.1007/3-540-13345-3_44

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13345-2

  • Online ISBN: 978-3-540-38886-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics