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Optimal Lower Bounds for Rank and Select Indexes

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Automata, Languages and Programming (ICALP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4051))

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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 \(\lg n\).

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References

  1. David, R.: Clark. Compact Pat Trees. PhD thesis, University of Waterloo (1996)

    Google Scholar 

  2. Guy Jacobson. Succinct Static Data Structures. PhD thesis, Carnegie Mellon University (January 1989)

    Google Scholar 

  3. Miltersen, P.B.: Lower bounds on the size of selection and rank indexes. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 11–12 (2005)

    Google Scholar 

  4. Munro, J.I., Raman, V., Rao, S.S.: Space efficient suffix trees. In: Arvind, V., Ramanujam, R. (eds.) FST TCS 1998. LNCS, vol. 1530, pp. 186–196. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  5. Munro, J.I., Raman, V., Rao, S.S.: Space efficient suffix trees. Journal of Algorithms 39(2), 205–222 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Raman, R., Raman, V., Rao, S.S.: Succinct indexable dictionaries with applications to encoding k-ary trees and multisets. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 233–242 (2002)

    Google Scholar 

  7. Widmayer, P.: Personal communication (2006)

    Google Scholar 

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Author information

Authors and Affiliations

  1. David R. Cheriton School of Computer Science, University of Waterloo,  

    Alexander Golynski

Authors
  1. Alexander Golynski
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Editors and Affiliations

  1. Dipartimento di Informatica, Università Ca’ Foscari, Venice

    Michele Bugliesi

  2. Interdisciplinary Institute for BroadBand Technology (IBBT), Belgium

    Bart Preneel

  3. ECS, University of Southampton, UK

    Vladimiro Sassone

  4. FB Informatik, Univ. Dortmund, LS2, 44221, Dortmund, Germany

    Ingo Wegener

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© 2006 Springer-Verlag Berlin Heidelberg

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Golynski, A. (2006). Optimal Lower Bounds for Rank and Select Indexes. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_33

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  • DOI: https://doi.org/10.1007/11786986_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35904-3

  • Online ISBN: 978-3-540-35905-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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