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Longest Common Extensions in Sublinear Space

  • Philip Bille
  • Inge Li Gørtz
  • Mathias Bæk Tejs Knudsen
  • Moshe Lewenstein
  • Hjalte Wedel VildhøjEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9133)

Abstract

The longest common extension problem (LCE problem) is to construct a data structure for an input string \(T\) of length \(n\) that supports \({\mathrm {LCE}}(i,j)\) queries. Such a query returns the length of the longest common prefix of the suffixes starting at positions \(i\) and \(j\) in \(T\). This classic problem has a well-known solution that uses \(\mathcal {O}(n)\) space and \(\mathcal {O}(1)\) query time. In this paper we show that for any trade-off parameter \(1 \le \tau \le n\), the problem can be solved in \(\mathcal {O}(\frac{n}{\tau })\) space and \(\mathcal {O}(\tau )\) query time. This significantly improves the previously best known time-space trade-offs, and almost matches the best known time-space product lower bound.

Keywords

Query Time Monte Carlo Algorithm Suffix Tree Input String Deterministic Solution 
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 International Publishing Switzerland 2015

Authors and Affiliations

  • Philip Bille
    • 1
  • Inge Li Gørtz
    • 1
  • Mathias Bæk Tejs Knudsen
    • 2
  • Moshe Lewenstein
    • 3
  • Hjalte Wedel Vildhøj
    • 1
    Email author
  1. 1.Technical University of Denmark, DTU ComputeLyngbyDenmark
  2. 2.Department of Computer ScienceUniversity of CopenhagenCopenhagenDenmark
  3. 3.Bar Ilan UniversityRamat GanIsrael

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