Article

Optimal lower bounds for rank and select indexes

Author:

Alexander GolynskiAuthors Info & Claims

ICALP'06: Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I

Pages 370 - 381

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

Published: 10 July 2006 Publication History

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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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Peter Bro Miltersen. Lower bounds on the size of selection and rank indexes. In Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 11-12, 2005.

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Cited By

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Navarro GProvidel E(2012)Fast, small, simple rank/select on bitmapsProceedings of the 11th international conference on Experimental Algorithms10.1007/978-3-642-30850-5_26(295-306)Online publication date: 7-Jun-2012
https://dl.acm.org/doi/10.1007/978-3-642-30850-5_26
Farzan AMunro J(2011)Succinct representation of dynamic treesTheoretical Computer Science10.1016/j.tcs.2010.10.030412:24(2668-2678)Online publication date: 1-May-2011
https://dl.acm.org/doi/10.1016/j.tcs.2010.10.030
Fischer JMäkinen VNavarro G(2009)Faster entropy-bounded compressed suffix treesTheoretical Computer Science10.1016/j.tcs.2009.09.012410:51(5354-5364)Online publication date: 1-Nov-2009
https://dl.acm.org/doi/10.1016/j.tcs.2009.09.012
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Published In

ICALP'06: Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I

July 2006

729 pages

ISBN:3540359044

Editors:
Michele Bugliesi
Dipartimento di Informatica, Università Ca' Foscari, Venice
,
Bart Preneel
Dipartimento di Informatica, Interdisciplinary Institute for BroadBand Technology (IBBT), Belgium
,
Vladimiro Sassone
ECS, University of Southampton, Belgium, UK
,
Ingo Wegener
FB Informatik, Univ. Dortmund, Dortmund, Germany

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 10 July 2006

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Navarro GProvidel E(2012)Fast, small, simple rank/select on bitmapsProceedings of the 11th international conference on Experimental Algorithms10.1007/978-3-642-30850-5_26(295-306)Online publication date: 7-Jun-2012
https://dl.acm.org/doi/10.1007/978-3-642-30850-5_26
Farzan AMunro J(2011)Succinct representation of dynamic treesTheoretical Computer Science10.1016/j.tcs.2010.10.030412:24(2668-2678)Online publication date: 1-May-2011
https://dl.acm.org/doi/10.1016/j.tcs.2010.10.030
Fischer JMäkinen VNavarro G(2009)Faster entropy-bounded compressed suffix treesTheoretical Computer Science10.1016/j.tcs.2009.09.012410:51(5354-5364)Online publication date: 1-Nov-2009
https://dl.acm.org/doi/10.1016/j.tcs.2009.09.012
Vigna S(2008)Broadword implementation of rank/select queriesProceedings of the 7th international conference on Experimental algorithms10.5555/1788888.1788900(154-168)Online publication date: 30-May-2008
https://dl.acm.org/doi/10.5555/1788888.1788900
Belazzougui DBoldi PPagh RVigna S(2008)Theory and practice of monotone minimal perfect hashingACM Journal of Experimental Algorithmics10.1145/1963190.202537816(3.1-3.26)Online publication date: 16-Nov-2008
https://dl.acm.org/doi/10.1145/1963190.2025378
Golynski AGrossi RGupta ARaman RRao S(2007)On the size of succinct indicesProceedings of the 15th annual European conference on Algorithms10.5555/1778580.1778616(371-382)Online publication date: 8-Oct-2007
https://dl.acm.org/doi/10.5555/1778580.1778616
Ferragina PVenturini RGabow H(2007)A simple storage scheme for strings achieving entropy boundsProceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms10.5555/1283383.1283457(690-696)Online publication date: 7-Jan-2007
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Navarro GMäkinen V(2007)Compressed full-text indexesACM Computing Surveys10.1145/1216370.121637239:1(2-es)Online publication date: 12-Apr-2007
https://dl.acm.org/doi/10.1145/1216370.1216372
Ferragina PVenturini R(2007)A simple storage scheme for strings achieving entropy boundsTheoretical Computer Science10.1016/j.tcs.2006.12.012372:1(115-121)Online publication date: 1-Mar-2007
https://dl.acm.org/doi/10.1016/j.tcs.2006.12.012

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