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International Symposium on String Processing and Information Retrieval

SPIRE 2018: String Processing and Information Retrieval pp 42–49Cite as

Longest Property-Preserved Common Factor

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 11147)

Abstract

In this paper we introduce a new family of string processing problems. We are given two or more strings and we are asked to compute a factor common to all strings that preserves a specific property and has maximal length. Here we consider two fundamental string properties: square-free factors and periodic factors under two different settings, one per property. In the first setting, we are given a string x and we are asked to construct a data structure over x answering the following type of on-line queries: given string y, find a longest square-free factor common to x and y. In the second setting, we are given k strings and an integer \(1 < k'\le k\) and we are asked to find a longest periodic factor common to at least \(k'\) strings. We present linear-time solutions for both settings. We anticipate that our paradigm can be extended to other string properties.

Keywords

  • Longest common factor
  • Periodicity
  • Squares
  • Algorithms

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References

  1. Ayad, L.A.K., Barton, C., Charalampopoulos, P., Iliopoulos, C.S., Pissis, S.P.: Longest common prefixes with \(k\)-errors and applications. In: Gagie, T., et al. (eds.) SPIRE 2018. LNCS, vol. 11147, pp. 27–41. Springer, Heidelberg (2018)

    Google Scholar 

  2. Bae, S.W., Lee, I.: On finding a longest common palindromic subsequence. Theor Comput Sci 710, 29–34 (2018). Advances in Algorithms and Combinatorics on Strings (Honoring 60th birthday for Prof. Costas S, Iliopoulos)

    MathSciNet  CrossRef  Google Scholar 

  3. Bannai, H., I, T., Inenaga, S., Nakashima, Y., Takeda, M., Tsuruta, K.: The “runs” theorem. SIAM J. Comput. 46(5), 1501–1514 (2017)

    MathSciNet  CrossRef  Google Scholar 

  4. Barton, C., Kociumaka, T., Liu, C., Pissis, S.P., Radoszewski, J.: Indexing weighted sequences: neat and efficient. CoRR, arXiv:abs/1704.07625 (2017)

  5. Belazzougui, D., Cunial, F.: Indexed matching statistics and shortest unique substrings. In: Moura, E., Crochemore, M. (eds.) SPIRE 2014. LNCS, vol. 8799, pp. 179–190. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11918-2_18

    CrossRef  Google Scholar 

  6. Chang, W.I., Lawler, E.L.: Sublinear approximate string matching and biological applications. Algorithmica 12(4), 327–344 (1994)

    MathSciNet  CrossRef  Google Scholar 

  7. Charalampopoulos, P., et al.: Linear-time algorithm for long LCF with K mismatches. In: CPM. LIPIcs, vol. 105, pp. 23:1–23:16. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2018)

    Google Scholar 

  8. Chi, L., Hui, K.: Color set size problem with applications to string matching. In: Apostolico, A., Crochemore, M., Galil, Z., Manber, U. (eds.) CPM 1992. LNCS, vol. 644, pp. 230–243. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-56024-6_19

    CrossRef  Google Scholar 

  9. Chowdhury, S.R., Hasan, M.M., Iqbal, S., Rahman, M.S.: Computing a longest common palindromic subsequence. Fundam. Inf. 129(4), 329–340 (2014)

    MathSciNet  MATH  Google Scholar 

  10. Dumitran, M., Manea, F., Nowotka, D.: On prefix/suffix-square free words. In: Iliopoulos, C., Puglisi, S., Yilmaz, E. (eds.) SPIRE 2015. LNCS, vol. 9309, pp. 54–66. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23826-5_6

    CrossRef  Google Scholar 

  11. Duval, J.-P., Kolpakov, R., Kucherov, G., Lecroq, T., Lefebvre, A.: Linear-time computation of local periods. Theor. Comput. Sci. 326(1), 229–240 (2004)

    MathSciNet  CrossRef  Google Scholar 

  12. Farach, M.: Optimal suffix tree construction with large alphabets. In: 38th Annual Symposium on Foundations of Computer Science (FOCS), pp. 137–143 (1997)

    Google Scholar 

  13. Farach, M., Muthukrishnan, S.: Perfect hashing for strings: formalization and algorithms. In: Hirschberg, D., Myers, G. (eds.) CPM 1996. LNCS, vol. 1075, pp. 130–140. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61258-0_11

    CrossRef  Google Scholar 

  14. Federico, M., Pisanti, N.: Suffix tree characterization of maximal motifs in biological sequences. Theor. Comput. Sci. 410(43), 4391–4401 (2009)

    MathSciNet  CrossRef  Google Scholar 

  15. Gusfield, D.: Algorithms on Strings, Trees, and Sequences - Computer Science and Computational Biology. Cambridge University Press, Cambridge (1997)

    CrossRef  Google Scholar 

  16. Inenaga, S., Hyyrö, H.: A hardness result and new algorithm for the longest common palindromic subsequence problem. Inf. Process. Lett. 129, 11–15 (2018)

    MathSciNet  CrossRef  Google Scholar 

  17. Inoue, T., Inenaga, S., Hyyrö, H., Bannai, H., Takeda, M.: Computing longest common square subsequences. In: 29th Symposium on Combinatorial Pattern Matching (CPM), LIPIcs, vol. 105, pp. 15:1–15:13 (2018)

    Google Scholar 

  18. Kociumaka, T., Starikovskaya, T., Vildhøj, H.W.: Sublinear space algorithms for the longest common substring problem. In: Schulz, A.S., Wagner, D. (eds.) ESA 2014. LNCS, vol. 8737, pp. 605–617. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44777-2_50

    CrossRef  MATH  Google Scholar 

  19. Kolpakov, R., Kucherov, G.: Finding maximal repetitions in a word in linear time. In: 40th Symposium on Foundations of Comp Science, pp. 596–604 (1999)

    Google Scholar 

  20. Lothaire, M.: Applied Combinatorics on Words. Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2005)

    CrossRef  Google Scholar 

  21. Peterlongo, P., Pisanti, N., Boyer, F., do Lago, A.P., Sagot, M.: Lossless filter for multiple repetitions with hamming distance. J. Discr. Alg. 6(3), 497–509 (2008)

    MathSciNet  CrossRef  Google Scholar 

  22. Peterlongo, P., Pisanti, N., Boyer, F., Sagot, M.-F.: Lossless filter for finding long multiple approximate repetitions using a new data structure, the Bi-factor array. In: Consens, M., Navarro, G. (eds.) SPIRE 2005. LNCS, vol. 3772, pp. 179–190. Springer, Heidelberg (2005). https://doi.org/10.1007/11575832_20

    CrossRef  Google Scholar 

  23. Starikovskaya, T., Vildhøj, H.W.: Time-space trade-offs for the longest common substring problem. In: Fischer, J., Sanders, P. (eds.) CPM 2013. LNCS, vol. 7922, pp. 223–234. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38905-4_22

    CrossRef  Google Scholar 

  24. Thankachan, S.V., Aluru, C., Chockalingam, S.P., Aluru, S.: Algorithmic framework for approximate matching under bounded edits with applications to sequence analysis. In: Raphael, B.J. (ed.) RECOMB 2018. LNCS, vol. 10812, pp. 211–224. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89929-9_14

    CrossRef  Google Scholar 

  25. Thankachan, S.V., Apostolico, A., Aluru, S.: A provably efficient algorithm for the k-mismatch average common substring problem. J. Comput. Biol. 23(6), 472–482 (2016)

    MathSciNet  CrossRef  Google Scholar 

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Acknowledgements

Solon P. Pissis and Giovanna Rosone are partially supported by the Royal Society project IE 161274 “Processing uncertain sequences: combinatorics and applications”. Giovanna Rosone and Nadia Pisanti are partially supported by the project Italian MIUR-SIR CMACBioSeq (“Combinatorial methods for analysis and compression of biological sequences”) grant n. RBSI146R5L.

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Authors and Affiliations

  1. Department of Informatics, King’s College London, London, UK

    Lorraine A. K. Ayad, Costas S. Iliopoulos & Solon P. Pissis

  2. Department of Informatics, Systems and Communication, University of Milan-Bicocca, Milan, Italy

    Giulia Bernardini

  3. Department of Computer Science, University of Pisa, Pisa, Italy

    Roberto Grossi, Nadia Pisanti & Giovanna Rosone

  4. ERABLE Team, INRIA, Lyon, France

    Nadia Pisanti

Authors
  1. Lorraine A. K. Ayad
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  2. Giulia Bernardini
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  3. Roberto Grossi
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  4. Costas S. Iliopoulos
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  5. Nadia Pisanti
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  6. Solon P. Pissis
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  7. Giovanna Rosone
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Corresponding author

Correspondence to Nadia Pisanti .

Editor information

Editors and Affiliations

  1. Diego Portales University, Santiago, Chile

    Travis Gagie

  2. The University of Melbourne, Melbourne, VIC, Australia

    Alistair Moffat

  3. University of Chile, Santiago, Chile

    Gonzalo Navarro

  4. Universidad de Ingeniería y Tecnología, Lima, Peru

    Ernesto Cuadros-Vargas

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Ayad, L.A.K. et al. (2018). Longest Property-Preserved Common Factor. In: Gagie, T., Moffat, A., Navarro, G., Cuadros-Vargas, E. (eds) String Processing and Information Retrieval. SPIRE 2018. Lecture Notes in Computer Science(), vol 11147. Springer, Cham. https://doi.org/10.1007/978-3-030-00479-8_4

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  • DOI: https://doi.org/10.1007/978-3-030-00479-8_4

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