Compressed String Dictionary Look-Up with Edit Distance One

  • Djamal Belazzougui
  • Rossano Venturini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7354)


In this paper we present different solutions for the problem of indexing a dictionary of strings in compressed space. Given a pattern P, the index has to report all the strings in the dictionary having edit distance at most one with P. Our first solution is able to solve queries in (almost optimal) O(|P| + occ) time where occ is the number of strings in the dictionary having edit distance at most one with P. The space complexity of this solution is bounded in terms of the k-th order entropy of the indexed dictionary. Our second solution further improves this space complexity at the cost of increasing the query time.


Space Complexity Edit Distance Query Time Alphabet Size Memory Word 
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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  1. 1.
    Belazzougui, D.: Faster and Space-Optimal Edit Distance “1” Dictionary. In: Kucherov, G., Ukkonen, E. (eds.) CPM 2009 Lille. LNCS, vol. 5577, pp. 154–167. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  2. 2.
    Belazzougui, D., Navarro, G.: Alphabet-Independent Compressed Text Indexing. In: Demetrescu, C., Halldórsson, M.M. (eds.) ESA 2011. LNCS, vol. 6942, pp. 748–759. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  3. 3.
    Brodal, G.S., G\k{a}sieniec, L.: Approximate Dictionary Queries. In: Hirschberg, D.S., Meyers, G. (eds.) CPM 1996. LNCS, vol. 1075, pp. 65–74. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  4. 4.
    Brodal, G.S., Srinivasan, V.: Improved bounds for dictionary look-up with one error. Information Processing Letters 75(1-2), 57–59 (2000)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Burrows, M., Wheeler, D.: A block sorting lossless data compression algorithm. Technical Report 124, Digital Equipment Corporation (1994)Google Scholar
  6. 6.
    Dietzfelbinger, M., Gil, J., Matias, Y., Pippenger, N.: Polynomial Hash Functions are Reliable (Extended abstract). In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623, pp. 235–246. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  7. 7.
    Elias, P.: Efficient storage and retrieval by content and address of static files. J. ACM 21, 246–260 (1974)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Fano, R.M.: On the number of bits required to implement an associative memory. Memorandum 61, Computer Structures Group, Project MAC (1971)Google Scholar
  9. 9.
    Ferragina, P., Venturini, R.: A simple storage scheme for strings achieving entropy bounds. Theor. Comput. Sci. 372(1), 115–121 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Ferragina, P., Venturini, R.: The compressed permuterm index. ACM Transactions on Algorithms 7(1), 10 (2010)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Fischer, J., Heun, V.: Space-efficient preprocessing schemes for range minimum queries on static arrays. SIAM J. Comput. 40(2), 465–492 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Hagerup, T., Tholey, T.: Efficient Minimal Perfect Hashing in Nearly Minimal Space. In: Ferreira, A., Reichel, H. (eds.) STACS 2001. LNCS, vol. 2010, pp. 317–326. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  13. 13.
    Karp, R.M., Rabin, M.O.: Efficient randomized pattern-matching algorithms. IBM Journal of Research and Development 31(2), 249–260 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Munro, J.I., Raman, V.: Succinct representation of balanced parentheses and static trees. SIAM J. Comput. 31(3), 762–776 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Russo, L.M.S., Navarro, G., Oliveira, A.L.: Fully compressed suffix trees. ACM Transactions on Algorithms 7(4), 53 (2011)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Sadakane, K.: Compressed suffix trees with full functionality. Theory Comput. Syst. 41(4), 589–607 (2007)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Djamal Belazzougui
    • 1
  • Rossano Venturini
    • 2
  1. 1.LIAFAUniv. Paris Diderot - Paris 7France
  2. 2.Dept. of Computer ScienceUniversity of PisaItaly

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