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Weak Binary Search Trees

Author Tobias Lauer

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LIPIcs.FUN.2026.28.pdf
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  • 12 pages

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Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
Keywords
  • Binary search trees
  • weak data structures
  • relaxed in-order invariant
  • balancing

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Abstract

Binary Search Trees (BST) have probably been studied more extensively than any other data structure in computer science. Their central property is the in-order invariant, which enables search for a key in time proportional to the height of the tree. Quite interestingly, the need for this strict invariant for efficient search seems to have always been taken for granted. In this paper, we introduce Weak Binary Search Trees (WST) and show that the in-order invariant can be relaxed substantially without sacrificing the O(log n) runtime bounds for search known from BST. 
We provide a simple and efficient search algorithm and list methods for insertion and deletion of keys in time proportional to the height of the tree. For balancing WST, rotations are less efficient than in BST. We adapt a rotation-free balancing scheme to WST, which can keep update operations in O(log n) overall time in the amortized average case.

Cite As Get BibTex

Tobias Lauer. Weak Binary Search Trees. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 28:1-28:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.FUN.2026.28

Author Details

Tobias Lauer
  • Offenburg University of Applied Sciences, Germany

Acknowledgements

Thanks are going to the anonymous reviewers for helpful comments and suggestions.

References

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