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Factorizing a String into Squares in Linear Time

Authors Yoshiaki Matsuoka, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda, Florin Manea

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Yoshiaki Matsuoka
Shunsuke Inenaga
Hideo Bannai
Masayuki Takeda
Florin Manea

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Yoshiaki Matsuoka, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda, and Florin Manea. Factorizing a String into Squares in Linear Time. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 27:1-27:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.CPM.2016.27

Abstract

A square factorization of a string w is a factorization of w in which each factor is a square. Dumitran et al. [SPIRE 2015, pp. 54-66] showed how to find a square factorization of a given string of length n in O(n log n) time, and they posed a question whether it can be done in O(n) time. In this paper, we answer their question positively, showing an O(n)-time algorithm for square factorization in the standard word RAM model with machine word size omega = Omega(log n). We also show an O(n + (n log^2 n) / omega)-time (respectively, O(n log n)-time) algorithm to find a square factorization which contains the maximum (respectively, minimum) number of squares.
Keywords
  • Squares
  • Runs
  • Factorization of Strings

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References

  1. Golnaz Badkobeh, Hideo Bannai, Keisuke Goto, Tomohiro I, Costas S. Iliopoulos, Shunsuke Inenaga, Simon J. Puglisi, and Shiho Sugimoto. Closed factorization. In Proc. PSC 2014, pages 162-168, 2014. Google Scholar
  2. Hideo Bannai, Travis Gagie, Shunsuke Inenaga, Juha Kärkkäinen, Dominik Kempa, Marcin Piatkowski, Simon J. Puglisi, and Shiho Sugimoto. Diverse palindromic factorization is np-complete. In Proc. DLT 2015, volume 9168 of Lecture Notes in Comput. Sci., pages 85-96. Springer, 2015. Google Scholar
  3. Hideo Bannai, Tomohiro I, Shunsuke Inenaga, Yuto Nakashima, Masayuki Takeda, and Kazuya Tsuruta. The "Runs" Theorem. CoRR, abs/1406.0263, 2014. URL: http://arxiv.org/abs/1406.0263.
  4. Maxime Crochemore. An optimal algorithm for computing the repetitions in a word. Inf. Process. Lett., 12(5):244-250, 1981. Google Scholar
  5. Maxime Crochemore, Lucian Ilie, and William F. Smyth. A simple algorithm for computing the lempel ziv factorization. In Proc. DCC 2008, pages 482-488. IEEE, 2008. Google Scholar
  6. Maxime Crochemore and Wojciech Rytter. Squares, cubes, and time-space efficient string searching. Algorithmica, 13(5):405-425, 1995. URL: http://dx.doi.org/10.1007/BF01190846.
  7. Marius Dumitran, Florin Manea, and Dirk Nowotka. On prefix/suffix-square free words. In Proc. SPIRE 2015, volume 9309 of Lecture Notes in Comput. Sci., pages 54-66. Springer, 2015. Google Scholar
  8. Jean-Pierre Duval. Factorizing words over an ordered alphabet. J. Algorithms, 4(4):363-381, 1983. URL: http://dx.doi.org/10.1016/0196-6774(83)90017-2.
  9. Gabriele Fici, Travis Gagie, Juha Kärkkäinen, and Dominik Kempa. A subquadratic algorithm for minimum palindromic factorization. J. Discrete Algorithms, 28:41-48, 2014. Google Scholar
  10. Jesús García-López, Florin Manea, and Victor Mitrana. Prefix-suffix duplication. J. Comput. Syst. Sci., 80(7):1254-1265, 2014. URL: http://dx.doi.org/10.1016/j.jcss.2014.02.011.
  11. Torben Hagerup. Sorting and searching on the word RAM. In Proc. STACS 1998, volume 1373 of Lecture Notes in Comput. Sci., pages 366-398. Springer, 1998. Google Scholar
  12. Tomohiro I, Shiho Sugimoto, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Computing palindromic factorizations and palindromic covers on-line. In Proc. CPM 2014,, volume 8486 of Lecture Notes in Comput. Sci., pages 150-161. Springer, 2014. Google Scholar
  13. Donald E. Knuth, James H. Morris Jr., and Vaughan R. Pratt. Fast pattern matching in strings. SIAM J. Comput., 6(2):323-350, 1977. URL: http://dx.doi.org/10.1137/0206024.
  14. Roman Kolpakov and Gregory Kucherov. Finding maximal repetitions in a word in linear time. In Proc. FOCS 1999, pages 596-604. IEEE, 1999. Google Scholar
  15. Dmitry Kosolobov, Mikhail Rubinchik, and Arseny M. Shur. Pal^k is linear recognizable online. In SOFSEM 2015, volume 8939 of Lecture Notes in Comput. Sci., pages 289-301. Springer, 2015. Google Scholar
  16. Manfred Kufleitner. On bijective variants of the Burrows-Wheeler transform. In Proc. PSC 2009, pages 65-79, 2009. Google Scholar
  17. Roger C. Lyndon. On Burnside’s problem. Trans. Amer. Math. Soc., 77(2):202-215, 1954. URL: http://www.jstor.org/stable/1990868.
  18. Michael G. Main and Richard J. Lorentz. An O(n log n) algorithm for finding all repetitions in a string. J. Algorithms, 5(3):422-432, 1984. Google Scholar
  19. James A. Storer and Thomas G. Szymanski. Data compression via textural substitution. J. ACM, 29(4):928-951, 1982. URL: http://dx.doi.org/10.1145/322344.322346.
  20. Terry A. Welch. A technique for high-performance data compression. IEEE Computer, 17(6):8-19, 1984. Google Scholar
  21. Jacob Ziv and Abraham Lempel. A universal algorithm for sequential data compression. IEEE Trans. Information Theory, 23(3):337-343, 1977. Google Scholar
  22. Jacob Ziv and Abraham Lempel. Compression of individual sequences via variable-rate coding. IEEE Trans. Information Theory, 24(5):530-536, 1978. Google Scholar
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