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Range LCP

  • Amihood Amir
  • Alberto Apostolico
  • Gad M. Landau
  • Avivit Levy
  • Moshe Lewenstein
  • Ely Porat
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)

Abstract

In this paper, we define the Range LCP problem as follows. Preprocess a string S, of length n, to enable efficient solutions of the following query:

Given \([i,j],\ \ 0< i \leq j \leq n\), compute max ℓ, k ∈ {i,…,j} LCP(S , S k ), where LCP(S , S k ) is the length of the longest common prefix of the suffixes of S starting at locations ℓ and k. This is a natural generalization of the classical LCP problem.

Surprisingly, while it is known how to preprocess a string in linear time to enable LCP computation of two suffixes in constant time, this seems quite difficult in the Range LCP problem. It is trivial to answer such queries in time O(|j − i|2) after a linear-time preprocessing and easy to show an O(1) query algorithm after an O(|S|2) time preprocessing. We provide algorithms that solve the problem with the following complexities:

  1. 1

    Preprocessing Time: O(|S|), Space: O(|S|), Query Time: O(|j − i|loglogn).

     
  2. 2

    Preprocessing Time: no preprocessing, Space: O(|j − i|log|j − i|), Query Time: O(|j − i|log|j − i|). However, the query just gives the pairs with the longest LCP, not the LCP itself.

     
  3. 3

    Preprocessing Time: O(|S|log2 |S|), Space: O(|S|log1 + ε |S|) for arbitrary small constant ε, Query Time: O(loglog|S|).

     

Keywords

Query Time Query Algorithm Preprocessing Time Succinct Representation Marked Leaf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Amihood Amir
    • 1
    • 2
  • Alberto Apostolico
    • 3
    • 4
  • Gad M. Landau
    • 5
    • 6
  • Avivit Levy
    • 7
    • 8
  • Moshe Lewenstein
    • 1
  • Ely Porat
    • 1
  1. 1.Department of Computer ScienceBar-Ilan UniversityRamat-GanIsrael
  2. 2.Department of Computer ScienceJohns Hopkins UniversityBaltimoreUSA
  3. 3.College of ComputingGeorgia Institute of TechnologyAtlantaUSA
  4. 4.Dipartimento di Ingegneria dell’ InformazioneUniversità diPadovaPadovaItaly
  5. 5.Department of Computer ScienceUniversity of HaifaMount CarmelIsrael
  6. 6.Department of Computer Science and EngineeringPolytechnic Institute of New York UniversityBrooklynUSA
  7. 7.Department of Software EngineeringShenkar CollegeRamat-GanIsrael
  8. 8.CRIHaifa UniversityMount CarmelIsrael

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