Randomization of search trees by subtree size

  • Salvador Roura
  • Conrado Martínez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1136)


In this paper we present randomized algorithms over binary search trees such that: a) the insertion of a set of keys in any fixed order into an initially empty tree always produces a random binary search tree; b) the deletion of any key from a random binary search tree results in a random binary search tree; c) the random choices made by the algorithms are based upon the sizes of the subtrees of the tree; this will imply that we will be able to support accesses by rank without additional storage requirements or modification of the data structures; and d) the cost of any elementary operation, measured as the number of visited nodes, is the same as the expected cost of its standard deterministic counterpart; hence, all operations have thus guaranteed expected cost O(log n), but now irrespective of any assumption on the input distribution.


Search Tree Deterministic Algorithm Binary Search Tree 30th Annual IEEE Symposium Left Subtree 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Salvador Roura
    • 1
  • Conrado Martínez
    • 1
  1. 1.Departament de Llenguatges i Sistemes InformáticsUniversitat Politècnica de CatalunyaBarcelonaSpain

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