Static Dictionaries Supporting Rank

  • Venkatesh Raman
  • S. Srinivasa Rao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1741)

Abstract

A static dictionary is a data structure for storing a subset S of a finite universe U so that membership queries can be answered efficiently. We explore space efficient structures to also find the rank of an element if found. We first give a representation of a static dictionary that takes n lg m + O(lg lg m) bits of space and supports membership and rank (of an element present in S) queries in constant time, where n = |S| and m = |U|. Using our structure we also give a representation of a m-ary cardinal tree with n nodes using n⌈lgm⌉ + 2n + o(n) bits of space that supports the tree navigational operations in O(1) time, when m is o(2lg n/ lg lg n ). For arbitrary m, we give a structure that takes the same space and supports all the navigational operations, except finding the child labeled i (for any i), in O(1) time. Finding the child labeled i in this structure takes O(lg lg lg m) time.

Keywords

Constant Time Hash Function Membership Query Auxiliary Structure Select Operation 
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 1999

Authors and Affiliations

  • Venkatesh Raman
    • 1
  • S. Srinivasa Rao
    • 1
  1. 1.C. I. T. CampusThe Institute of Mathematical SciencesChennaiIndia

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