Acta Informatica

, Volume 37, Issue 10, pp 743–763 | Cite as

Relaxed balance for search trees with local rebalancing

  • Kim S. Larsen
  • Thomas Ottmann
  • Eljas Soisalon-Soininen
Original articles


Search trees with relaxed balance were introduced with the aim of facilitating fast updating on shared-memory asynchronous parallel architectures. To obtain this, rebalancing has been uncoupled from the updating, so extensive locking in connection with updates is avoided. Rebalancing is taken care of by background processes, which do only a constant amount of work at a time before they release locks. Thus, the rebalancing and the associated locks are very localized in time as well as in space. In particular, there is no exclusive locking of whole paths. This means that the amount of parallelism possible is not limited by the height of the tree.

Search trees with relaxed balance have been obtained by adapting standard sequential search trees to this new paradigm; clearly using similar techniques in each case, but no general result has been obtained. We show how any search tree with local bottom-up rebalancing can be used in a relaxed variant, preserving the complexity of the rebalancing from the sequential case. Additionally, we single out the one high level locking mechanism that a parallel implementation must provide in order to guarantee cons istency.

Though the ideas have come from search trees, the result presented here applies to tree structures in general, where operations initiated at the leaves progress towards the root in constant-sized steps.


General Result Tree Structure Search Tree Similar Technique Parallel Implementation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Kim S. Larsen
    • 1
  • Thomas Ottmann
    • 2
  • Eljas Soisalon-Soininen
    • 3
  1. 1.Department of Mathematics and Computer Science, University of Southern Denmark, Main campus: Odense University, Campusvej 55, 5230 Odense M, Denmark (e-mail: DK
  2. 2.Institute of Computer Science, Freiburg University, Am Flughafen 17, 79110 Freiburg, Germany (e-mail: DE
  3. 3.Laboratory of Information Processing Science, Helsinki University of Technology, Otakaari 1 A, 02150 Espoo, Finland (e-mail: FI

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