Predecessor queries in dynamic integer sets

  • Gerth Stølting Brodal
Algorithms I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1200)

Abstract

We consider the problem of maintaining a set of n integers in the range 0.2w−1 under the operations of insertion, deletion, predecessor queries, minimum queries and maximum queries on a unit cost RAM with word size w bits. Let f (n) be an arbitrary nondecreasing smooth function satisfying \(n \leqslant f(n) \leqslant \sqrt {log n} \). A data structure is presented supporting insertions and deletions in worst case O(f(n)) time, predecessor queries in worst case O((logn)/f(n)) time and minimum and maximum queries in worst case constant time. The required space is O(n2w) for an arbitrary constant ∈ > 0. The RAM operations used are addition, arbitrary left and right bit shifts and bit-wise boolean operations. The data structure is the first supporting predecessor queries in worst case O(log n/log log n) time while having worst case O(log log n) update time.

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Gerth Stølting Brodal
    • 1
  1. 1.Basic Research in Computer Science, a Centre of the Danish National Research Foundation, Department of Computer ScienceUniversity of AarhusÅrhus CDenmark

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