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Optimal In-Place Suffix Sorting

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String Processing and Information Retrieval (SPIRE 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11147))

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Abstract

The suffix array is a fundamental data structure for many applications that involve string searching and data compression. Designing time/space-efficient suffix array construction algorithms has attracted significant attentions and considerable advances have been made for the past 20 years. We obtain the first in-place linear time suffix array construction algorithms that are optimal both in time and space for (read-only) integer alphabets. Our algorithm settles the open problem posed by Franceschini and Muthukrishnan in ICALP 2007. The open problem asked to design in-place algorithms in \(o(n\log n)\) time and ultimately, in O(n) time for (read-only) integer alphabets with \(|\varSigma | \le n\). Our result is in fact slightly stronger since we allow \(|\varSigma |=O(n)\). Besides, we provide an optimal in-place \(O(n\log n)\) time suffix sorting algorithm for read-only general alphabets (i.e., only comparisons are allowed), recovering the result obtained by Franceschini and Muthukrishnan which was an open problem posed by Manzini and Ferragina in ESA 2002.

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Notes

  1. 1.

    Some previous algorithms state the space usages in terms of bits. We convert them into words.

  2. 2.

    The definitions of bucket array and type array can be found in Sect. 2.

  3. 3.

    Some previous papers use $ to denote the sentinel.

  4. 4.

    If one worries the \(O(\log n)\) workspace in the recursion, one can use the highest bits in \(\mathsf {SA}\) (i.e., n bits) to store them since the size of the reduced sub-problem is no larger than n/2.

  5. 5.

    We use at most five special symbols in this paper. The special symbol is only used to simplify the argument and we do not have to impose any additional assumption to accommodate these symbols (including the read-only general alphabets case). These special symbols can be handled using an extra O(1) workspace. The details can be found in our full version [24].

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Acknowledgments

This research is supported in part by the National Basic Research Program of China Grant 2015CB358700, the National Natural Science Foundation of China Grant 61772297, 61632016, 61761146003, and a grant from Microsoft Research Asia. The authors would like to thank Ge Nong for his help in our experiments, and Gonzalo Navarro for helpful suggestions.

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Authors and Affiliations

  1. Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China

    Zhize Li & Jian Li

  2. Department of Computer Science, Xidian University, Xi’an, China

    Hongwei Huo

Authors
  1. Zhize Li
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  2. Jian Li
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  3. Hongwei Huo
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Corresponding authors

Correspondence to Zhize Li or Jian Li .

Editor information

Editors and Affiliations

  1. Diego Portales University, Santiago, Chile

    Travis Gagie

  2. The University of Melbourne, Melbourne, VIC, Australia

    Alistair Moffat

  3. University of Chile, Santiago, Chile

    Gonzalo Navarro

  4. Universidad de Ingeniería y Tecnología, Lima, Peru

    Ernesto Cuadros-Vargas

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Li, Z., Li, J., Huo, H. (2018). Optimal In-Place Suffix Sorting. In: Gagie, T., Moffat, A., Navarro, G., Cuadros-Vargas, E. (eds) String Processing and Information Retrieval. SPIRE 2018. Lecture Notes in Computer Science(), vol 11147. Springer, Cham. https://doi.org/10.1007/978-3-030-00479-8_22

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  • DOI: https://doi.org/10.1007/978-3-030-00479-8_22

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