Acta Informatica

, Volume 21, Issue 1, pp 101–112 | Cite as

Maintaining order in a generalized linked list

  • Athanasios K. Tsakalidis


We give a representation for linked lists which allows to efficiently insert and delete objects in the list and to quickly determine the order of two list elements. The basic data structure, called an indexed BB [α]-tree, allows to do n insertions and deletions in O(n log n) steps and determine the order in constant time, assuming that the locations of the elements worked at are given. The improved algorithm does n insertions and deletions in O(n) steps and determines the order in constant time. An application of this provides an algorithm which determines the ancestor relationship of two given nodes in a dynamic tree structure of bounded degree in time O(1) and performs n arbitrary insertions and deletions at given positions in time O(n) using linear space.


Information System Operating System Data Structure Communication Network Constant Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Blum, N., Mehlhorn, K.: On the average number of rebalancing operations in weight-balanced trees. Theor. Comput. Sci. 11, 303–320 (1980)Google Scholar
  2. 2.
    Dietz, P.: Maintaining order in a linked list. 14th annual ACM Symposium on Theory of Computing, pp. 122–127, 1982Google Scholar
  3. 3.
    Huddleston, S., Mehlhorn, K.: A new data structure for representing sorted lists. Acta Informat. 17, 157–184 (1982)Google Scholar
  4. 4.
    Lengauer, Th., Mehlhorn, K.: HILL-Hierarchical layout language, A CAD-system for VLSI-design. Technischer Bericht A 82/10, Universität des Saarlandes, 1982Google Scholar
  5. 5.
    Maier, D.: An efficient method for storing ancestor information in trees. SIAM J. Comput. 8, 599–618 (1979)Google Scholar
  6. 6.
    Mehlhorn, K.: Effiziente Algorithmen. Stuttgart: Teubner 1977Google Scholar
  7. 7.
    Nievergelt, J., Reingold, E.M.: Binary search trees of bounded balance. SIAM J. Comput. 2, 33–43 (1973)Google Scholar
  8. 8.
    Overmars, M.: A O(1) average time update scheme for balanced search trees. Bull. EATCS, pp. 27–29 (1982)Google Scholar
  9. 9.
    Tsakalidis, A.: Maintaining order in a generalized linked list. 6th GI-Conference on Theoretical Computer Science, Dortmund LNCS, Vol. 145, pp. 343–352, 1983Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Athanasios K. Tsakalidis
    • 1
  1. 1.Fachbereich 10, Angewandte Mathematik und InformatikUniversität des SaarlandesSaarbrückenGermany

Personalised recommendations