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Rank and Select Operations on Bit Strings

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  • First Online:
Encyclopedia of Algorithms

Years and Authors of Summarized Original Work

  • 1974; Elias

  • 1989; Jacobson

  • 1998; Clark

  • 2007; Raman, Raman, Rao

  • 2008; PÇŽtraÅŸcu

  • 2014; Golynski, Orlandi, Raman, Rao

Problem Definition

Given a static bit string \(\boldsymbol{b} = b_{1}\ldots b_{m}\), the objective is to preprocess \(\boldsymbol{b}\) and to create a space-efficient data structure that supports the following operations rapidly:

rank1 (i):

takes an index i as input, 1 ≤ i ≤ m, and returns the number of 1s among b1… b i .

select1 (i):

takes an index i ≥ 1 as input and returns the position of the i-th 1 in \(\boldsymbol{b}\), and − 1 if i is greater than the number of 1s in \(\boldsymbol{b}\).

A data structure that supports the operations above will be called a bit vector. The operations rank0 and select0 are defined analogously for the 0s in \(\boldsymbol{b}\). As \(\textsf{rank}_{0}(i) = i -\textsf{rank}_{1}(i)\), one considers just rank1 (abbreviated to rank) and refers to select0 and select1 collectively as select. In what...

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Authors and Affiliations

  1. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Rajeev Raman

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  1. Rajeev Raman
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Correspondence to Rajeev Raman .

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Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Raman, R. (2016). Rank and Select Operations on Bit Strings. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_332

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