Combining Binary Search Trees

  • Erik D. Demaine
  • John Iacono
  • Stefan Langerman
  • Özgür Özkan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7965)


We present a general transformation for combining a constant number of binary search tree data structures (BSTs) into a single BST whose running time is within a constant factor of the minimum of any “well-behaved” bound on the running time of the given BSTs, for any online access sequence. (A BST has a well-behaved bound with f(n) overhead if it spends at most \(\mathcal{O}(f(n))\) time per access and its bound satisfies a weak sense of closure under subsequences.) In particular, we obtain a BST data structure that is \(\mathcal{O}(\log\log n)\) competitive, satisfies the working set bound (and thus satisfies the static finger bound and the static optimality bound), satisfies the dynamic finger bound, satisfies the unified bound with an additive \(\mathcal{O}(\log\log n)\) factor, and performs each access in worst-case \(\mathcal{O}(\log n)\) time.


Constant Number Steiner Tree Binary Search Tree Brute Force Search Splay Tree 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Erik D. Demaine
    • 1
  • John Iacono
    • 2
  • Stefan Langerman
    • 3
  • Özgür Özkan
    • 2
  1. 1.Massachusetts Institute of TechnologyUSA
  2. 2.Polytechnic Institute of New York UniversityUSA
  3. 3.Université Libre de BruxellesBelgium

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