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Optimal Lower Bounds for Rank and Select Indexes

  • Alexander Golynski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)

Abstract

We develop a new lower bound technique for data structures. We show an optimal \(\Omega(n \lg\lg n / \lg n)\) space lower bounds for storing an index that allows to implement rank and select queries on a bit vector B provided that B is stored explicitly. These results improve upon [Miltersen, SODA’05]. We show \(\Omega((m/t) \lg t)\) lower bounds for storing rank/select index in the case where B has m 1-bits in it (e.g. low 0-th entropy) and the algorithm is allowed to probe t bits of B. We simplify the select index given in [Raman et al., SODA’02] and show how to implement both rank and select queries with an index of size \((1 + o(1)) (n \lg\lg n / \lg n) + O(n / \lg n)\) (i.e. we give an explicit constant for storage) in the RAM model with word size \(\lg n\).

Keywords

Select Index Rank Index Word Probe Word Size Lower Block 
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 2006

Authors and Affiliations

  • Alexander Golynski
    • 1
  1. 1.David R. Cheriton School of Computer ScienceUniversity of Waterloo 

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