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A new data structure for representing sorted lists

  • Kurt Mehlhorn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 100)

Abstract

In this paper we explore the use of weak B-trees to represent sorted lists. In weak B-trees each node has at least a and at most b sons where 2a ≤ b. We analyse the worst case cost of sequences of insertions and deletions in weak B-trees. This leads to a new data structure (level-linked weak B-trees) for representing sorted lists when the access pattern exhibits a (time-varying) locality of reference. Our structure is substantially simpler than the one proposed by Guibas, McCreight, Plass and Roberts, yet it has many of its properties. Our structure is as simple as the one proposed by Brown/Tarjan, but our structure can treat arbitrary sequences of insertions and deletions whilst theirs can only treat non-interacting insertions and deletions.

Keywords

Arbitrary Sequence Interior Node Balance Tree Splitting Algorithm Node Splitting 
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.

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References

  1. Bayer/McCreight: "Organization and Maintenance of Large Ordered Indizes", Acta Informatica 1 (1972), 173–189Google Scholar
  2. Blum/Mehlhorn: "On the Average Number of Rebalancing Steps in Weight-Balanced Trees", 4th GI-Conference on Theoretical Computer Science, Aachen 1979, LNCS Vol. 67, 67–78Google Scholar
  3. Brown/Tarjan: "A Representation for Linear Lists with Movable Fingers", 10th ACM Symposium on Theory of Computing, p. 19–28, 1978Google Scholar
  4. Guibas/McCreight/Plass/Roberts: "A new representation for linear lists", 9th ACM Symposium on Theory of Computing, 1977, 49–60Google Scholar
  5. Mehlhorn: "Effiziente Algorithmen", Teubner-Verlag, Studienbücher Informatik, 1977Google Scholar
  6. Mehlhorn 79a: "Sorting Presorted Files", 4th GI-Conference on Theoretical Computer Science, Aachen 1979, LNCS, Vol. 67, p. 199–212Google Scholar
  7. Mehlhorn 79b: "Searching, Sorting and Information Theory", MFCS 79, Springer Lecture Notes in Computer Science, Vol. 74, p. 131–145Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Kurt Mehlhorn
    • 1
  1. 1.FB 10 — Informatik Universität des SaarlandesSaarbrücken

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