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Search Trees with Relaxed Balance and Near-Optimal Height

  • Rolf Fagerberg
  • Rune E. Jensen
  • Kim S. Larsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2125)

Abstract

We introduce the relaxed k-tree, a search tree with relaxed balance and a height bound, when in balance, of (1 + ε)log2n + 1, for any g > 0. The rebalancing work is amortized O(1/ε) per update. This is the first binary search tree with relaxed balance having a height bound better than c · log2 n for a fixed constant c. In all previous proposals, the constant is at least 1/log2 φ τ; 1.44, where φ is the golden ratio.

As a consequence, we can also define a standard (non-relaxed) k-tree with amortized constant rebalancing per update, which is an improvement over the original definition.

Search engines based on main-memory databases with strongly fluctuating workloads are possible applications for this line of work.

Keywords

Neighboring Node Search Tree Binary Search Tree Black Node External Node 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Rolf Fagerberg
    • 1
  • Rune E. Jensen
    • 2
  • Kim S. Larsen
    • 3
  1. 1.BRICS, Department of Computer ScienceUniversity of AarhusÅrhus CDenmark
  2. 2.ALOC Bonnier A/SOdense CDenmark
  3. 3.Department of Mathematics and Computer ScienceUniversity of Southern Denmark Main Campus: Odense UniversityOdense MDenmark

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