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A Linear-Space Data Structure for Range-LCP Queries in Poly-Logarithmic Time

  • Paniz Abedin
  • Arnab Ganguly
  • Wing-Kai Hon
  • Yakov Nekrich
  • Kunihiko Sadakane
  • Rahul Shah
  • Sharma V. ThankachanEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10976)

Abstract

Let \(\mathsf {T}[1,n]\) be a text of length n and \(\mathsf {T}[i,n]\) be the suffix starting at position i. Also, for any two strings X and Y, let \(\mathsf {LCP}(X, Y)\) denote their longest common prefix. The range-LCP of \(\mathsf {T}\) w.r.t. a range \([\alpha ,\beta ]\), where \(1\le \alpha < \beta \le n\) is Amir et al. [ISAAC 2011] introduced the indexing version of this problem, where the task is to build a data structure over \(\mathsf {T}\), so that \(\mathsf {rlcp}(\alpha ,\beta )\) for any query range \([\alpha ,\beta ]\) can be reported efficiently. They proposed an \(O(n\log ^{1+\epsilon } n)\) space structure with query time \(O(\log \log n)\), and a linear space (i.e., O(n) words) structure with query time \(O(\delta \log \log n)\), where \(\delta = \beta -\alpha +1\) is the length of the input range and \(\epsilon > 0\) is an arbitrarily small constant. Later, Patil et al. [SPIRE 2013] proposed another linear space structure with an improved query time of \(O(\sqrt{\delta }\log ^{\epsilon } \delta )\). This poses an interesting question, whether it is possible to answer \(\mathsf {rlcp}(\cdot ,\cdot )\) queries in poly-logarithmic time using a linear space data structure. In this paper, we settle this question by presenting an O(n) space data structure with query time \(O(\log ^{1+\epsilon } n)\) and construction time \(O(n\log n)\).

Notes

Acknowledgments

This research is supported in part by the U.S. NSF under the grants CCF-1703489 and CCF-1527435, and the Taiwan Ministry of Science and Technology under the grant 105-2221-E-007-040-MY3.

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Copyright information

© This is a U.S. government work and its text is not subject to copyright protection in the United States; however, its text may be subject to foreign copyright protection 2018

Authors and Affiliations

  • Paniz Abedin
    • 1
  • Arnab Ganguly
    • 2
  • Wing-Kai Hon
    • 3
  • Yakov Nekrich
    • 4
  • Kunihiko Sadakane
    • 5
  • Rahul Shah
    • 6
    • 7
  • Sharma V. Thankachan
    • 1
    Email author
  1. 1.Department of Computer ScienceUniversity of Central FloridaOrlandoUSA
  2. 2.Department of Computer ScienceUniversity of Wisconsin - WhitewaterWhitewaterUSA
  3. 3.Department of Computer ScienceNational Tsing Hua UniversityHsinchuTaiwan
  4. 4.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  5. 5.Department of Computer ScienceThe University of TokyoTokyoJapan
  6. 6.Department of Computer ScienceLouisiana State UniversityBaton RougeUSA
  7. 7.National Science Foundation (NSF)AlexandriaUSA

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