Efficient Implementation of Rank and Select Functions for Succinct Representation

  • Dong Kyue Kim
  • Joong Chae Na
  • Ji Eun Kim
  • Kunsoo Park
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3503)

Abstract

Succinct representation is a space-efficient method to represent n discrete objects by O(n) bits. In order to access directly the ith object of succinctly represented data structures in constant time, two fundamental functions, rank and select are commonly used. However, little efforts were made on analyzing practical behaviors of these functions despite their importance for succinct representations.

In this paper we analyze the behavior of Clark’s algorithm which is the only one to support select in constant time using o(n)-bit space of extra space, and show that the performance of Clark’s algorithm gets worse as the number of 1’s in a bit-string becomes fewer and there exists a worst case in which a large amount of operations are needed. Then, we propose two algorithms that overcome the drawbacks of Clark’s. These algorithms take constant time forselect, and one uses o(n) bits for extra space and the other uses n + o(n) bits in the worst case. Experimental results show that our algorithms compute select faster than Clark’s.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Dong Kyue Kim
    • 1
  • Joong Chae Na
    • 2
  • Ji Eun Kim
    • 1
  • Kunsoo Park
    • 2
  1. 1.School of Electrical and Computer EngineeringPusan National University 
  2. 2.School of Computer Science and EngineeringSeoul National University 

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