Inducing the LCP-Array

  • Johannes Fischer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6844)


We show how to modify the linear-time construction algorithm for suffix arrays based on induced sorting (Nong et al., DCC’09) such that it computes the array of longest common prefixes (LCP-array) as well. Practical tests show that this outperforms recent LCP-array construction algorithms (Gog and Ohlebusch, ALENEX’11).


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  1. 1.
    Alstrup, S., Gavoille, C., Kaplan, H., Rauhe, T.: Nearest common ancestors: A survey and a new algorithm for a distributed environment. Theory Comput. Syst. 37, 441–456 (2004)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Antonitio, R.P.J., Smyth, W.F., Turpin, A., Yu, X.: New suffix array algorithms — linear but not fast? In: Proc. Fifteenth Australasian Workshop Combinatorial Algorithms (AWOCA), pp. 148–156 (2004)Google Scholar
  3. 3.
    Cole, R., Hariharan, R.: Dynamic LCA queries on trees. SIAM J. Comput. 34(4), 894–923 (2005)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Fischer, J.: Optimal succinctness for range minimum queries. In: López-Ortiz, A. (ed.) LATIN 2010. LNCS, vol. 6034, pp. 158–169. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Fischer, J., Heun, V.: A new succinct representation of RMQ-information and improvements in the enhanced suffix array. In: Chen, B., Paterson, M., Zhang, G. (eds.) ESCAPE 2007. LNCS, vol. 4614, pp. 459–470. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Gabow, H.N., Bentley, J.L., Tarjan, R.E.: Scaling and related techniques for geometry problems. In: Proc. STOC, pp. 135–143. ACM Press, New York (1984)Google Scholar
  7. 7.
    Gog, S., Ohlebusch, E.: Fast and lightweight LCP-array construction algorithms. In: Proc. ALENEX, pp. 25–34. SIAM Press, Philadelphia (2011)Google Scholar
  8. 8.
    Harel, D., Tarjan, R.E.: Fast algorithms for finding nearest common ancestors. SIAM J. Comput. 13(2), 338–355 (1984); See also FOCS 1980MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Itoh, H., Tanaka, H.: An efficient method for in memory construction of suffix arrays. In: Proc. SPIRE/CRIWG, pp. 81–88. IEEE Press, Los Alamitos (1999)Google Scholar
  10. 10.
    Kärkkäinen, J., Manzini, G., Puglisi, S.J.: Permuted longest-common-prefix array. In: Kucherov, G., Ukkonen, E. (eds.) CPM 2009 Lille. LNCS, vol. 5577, pp. 181–192. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Kärkkäinen, J., Sanders, P., Burkhardt, S.: Linear work suffix array construction. J. ACM 53(6), 1–19 (2006)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Kasai, T., Lee, G., 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
  13. 13.
    Kim, D.K., Sim, J.S., Park, H., Park, K.: Constructing suffix arrays in linear time. J. Discrete Algorithms 3(2-4), 126–142 (2005)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Ko, P., Aluru, S.: Space efficient linear time construction of suffix arrays. J. Discrete Algorithms 3(2-4), 143–156 (2005)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Manber, U., Myers, E.W.: Suffix arrays: A new method for on-line string searches. SIAM J. Comput. 22(5), 935–948 (1993)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Manzini, G.: Two space saving tricks for linear time LCP array computation. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 372–383. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. 17.
    Navarro, G., Mäkinen, V.: Compressed full-text indexes. ACM Computing Surveys 39(1), Article No. 2 (2007)CrossRefMATHGoogle Scholar
  18. 18.
    Nong, G., Zhang, S., Chan, W.H.: Linear suffix array construction by almost pure induced-sorting. In: Proc. DCC, pp. 193–202. IEEE Press, Los Alamitos (2009)Google Scholar
  19. 19.
    Okanohara, D., Sadakane, K.: A linear-time burrows-wheeler transform using induced sorting. In: Karlgren, J., Tarhio, J., Hyyrö, H. (eds.) SPIRE 2009. LNCS, vol. 5721, pp. 90–101. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  20. 20.
    Puglisi, S.J., Smyth, W.F., Turpin, A.: A taxonomy of suffix array construction algorithms. ACM Computing Surveys 39(2) (2007)Google Scholar
  21. 21.
    Sadakane, K.: Compressed suffix trees with full functionality. Theory of Computing Systems 41(4), 589–607 (2007)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Seward, J.: On the performance of BWT sorting algorithms. In: Proc. DCC, pp. 173–182. IEEE Press, Los Alamitos (2000)Google Scholar
  23. 23.
    Weiner, P.: Linear pattern matching algorithms. In: Proc. Annual Symp. on Switching and Automata Theory, pp. 1–11. IEEE Computer Society, Los Alamitos (1973)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Johannes Fischer
    • 1
  1. 1.KITInstitut für Theoretische InformatikKarlsruheGermany

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