Shortest Unique Substring Query Revisited

  • Atalay Mert İleri
  • M. Oğuzhan Külekci
  • Bojian Xu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8486)

Abstract

We revisit the problem of finding shortest unique substring (SUS) proposed recently by Pei et al. (ICDE’13). We propose an optimal O(n) time and space algorithm that can find an SUS for every location of a string of size n and thus significantly improve their O(n 2) time complexity. Our method also supports finding all the SUSes covering every location, whereas theirs can find only one SUS for every location. Further, our solution is simpler and easier to implement and can also be more space efficient in practice, since we only use the inverse suffix array and the longest common prefix array of the string, while their algorithm uses the suffix tree of the string and other auxiliary data structures. Our theoretical results are validated by an empirical study that shows our method is much faster and more space-saving.

Keywords

shortest unique substring repetitiveness regularity 

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References

  1. 1.
    Crochemore, M., Rytter, W.: Jewels of stringology. World Scientific (2003)Google Scholar
  2. 2.
    İleri, A.M., Külekci, M.O., Xu, B.: Shortest unique substring query revisited, http://arxiv.org/abs/1312.2738
  3. 3.
    Kasai, T., Lee, G.H., Arimura, H., Arikawa, S., Park, K.: Linear-time longest-common-prefix computation in suffix arrays and its applications. In: Amir, A., Landau, G.M. (eds.) CPM 2001. LNCS, vol. 2089, pp. 181–192. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Ko, P., Aluru, S.: Space efficient linear time construction of suffix arrays. Journal of Discrete Algorithms 3(2-4), 143–156 (2005)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Pei, J., Wu, W.C.H., Yeh, M.Y.: On shortest unique substring queries. In: Proceedings of the 2013 IEEE International Conference on Data Engineering (ICDE), pp. 937–948 (2013)Google Scholar
  6. 6.
    Tsuruta, K., Inenaga, S., Bannai, H., Takeda, M.: Shortest unique substrings queries in optimal time. In: Geffert, V., Preneel, B., Rovan, B., Štuller, J., Tjoa, A.M. (eds.) SOFSEM 2014. LNCS, vol. 8327, pp. 503–513. Springer, Heidelberg (2014)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Atalay Mert İleri
    • 1
  • M. Oğuzhan Külekci
    • 2
  • Bojian Xu
    • 3
  1. 1.Department of Computer EngineeringBilkent UniversityTurkey
  2. 2.TÜBİTAK National Research Institute of Electronics and CryptologyTurkey
  3. 3.Department of Computer ScienceEastern Washington UniversityUSA

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