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Parallel Algorithms for Combinatorial Pattern Matching

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Combinatorial Image Analysis (IWCIA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8466))

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Abstract

In this talk we discuss on parallel computation approach to two-dimensional combinatorial pattern matching. The latter features numerous applications in pattern recognition, low level image processing, computer vision and, more recently, multimedia. After introducing some basic notions and concepts and recalling related key facts, we briefly discuss the basic steps of a parallel algorithm design, illustrating them by author’s results on the problem of detecting all two-dimensional repetitions in a two-dimensional array.

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References

  1. Amir, A., Benson, G.: Two-dimensional periodicity and its applications. In: Proc. 3rd ACM-SIAM Symp. on Discrete Algorithms, pp. 440–452 (1992)

    Google Scholar 

  2. Amir, A., Benson, G., Farach, M.: An alphabet independent approach to two-dimensional pattern matching. SIAM J. Comput. 23(2), 313–323 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  3. Apostolico, A.: Optimal parallel detection of squares in strings. Algorithmica 8, 285–319 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  4. Apostolico, A., Breslauer, D.: An optimal O(loglogn) time parallel algorithm for detecting all squares in strings. SIAM J. Comput. 25(6), 1318–1331 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  5. Apostolico, A., Brimkov, V.E.: Fibonacci arrays and their two-dimensional repetitions. Theoret. Comput. Sci. 237, 263–273 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Apostolico, A., Brimkov, V.E.: Optimal discovery of repetitions in 2D. Discrete Applied Mathematics 151, 5–20 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. Apostolico, A., Preparata, F.P.: Optimal off-line detection of repetitions in a string. Theoret. Comput. Sci. 22, 297–315 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  8. Apostolico, A., Preparata, F.P.: Structural properties of the string statistic problem. J. Comput. Systems 31(3), 394–411 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  9. Berthé, V., Vuillon, L.: Tilings and rotations on the torus: a two-dimensional generalization of Sturmian words. Discrete Mathematics 223, 27–53 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  10. Brent, R.P.: Evaluation of general arithmetic expressions. J. ACM 21, 201–206 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  11. Brimkov, V.E.: Optimally fast CRCW-PRAM testing 2D-arrays for existence of repetitive patterns. International Journal of Pattern Recognition and Artificial Intelligence 15(7), 1167–1182 (2001)

    Article  Google Scholar 

  12. Brimkov, V.E.: Optimal parallel searching an array for certain repetitions. E.N. Discr. Math. 12 (2003), http://www.elsevier.nl/gej-ng/31/29/24/show/Products/notes/contents.htt

  13. Brimkov, V.E., Barneva, R.P.: Plane digitization and related combinatorial problems. Discrete Applied Mathematics 147, 169–186 (2005); See also: Brimkov, V.E.: Digital flatness and related combinatorial problems. CITR-TR-120, University of Auckland, New Zealand, 45 pages (2002), http://www.citr.auckland.ac.nz/techreports/?year=2002

    Google Scholar 

  14. Cassaigne, J.: Two-dimensional sequences of complexity mn + 1. J. Automatic Language Combinatorics 4, 153–170 (1999)

    MATH  MathSciNet  Google Scholar 

  15. Cole, R., Crochemore, M., Galil, Z., Gąsieniec, L., Hariharan, R., Muthukrishnan, S., Park, K., Rytter, W.: Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions. In: Proc. 34th IEEE Symp. Found. Computer Science, pp. 248–258 (1993)

    Google Scholar 

  16. Crochemore, M.: An optimal algorithm for computing the repetitions in a word. Inform. Process. Let. 12(5), 244–250 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  17. Crochemore, M.: Transducers and repetitions. Theoret. Comput. Sci. 12, 63–86 (1986)

    Article  MathSciNet  Google Scholar 

  18. Epifanio, C., Koskas, M., Mignosi, F.: On a conjecture on bidimensional words. Theoretical Computer Science 299(1-3), 123–150 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  19. Fich, F.: The complexity of computation on the parallel random access machine (Chapter 21). In: Reif, J. (ed.) Synthesis of Parallel Algorithms. Morgan Kaufmann (1993)

    Google Scholar 

  20. Fich, F., Ragde, P., Wigderson, A.: Relations between CR-models of parallel computations. SIAM J. Comput. 17(3), 606–627 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  21. Galil, Z., Park, K.: Truly alphabet-independent two-dimensional pattern matching. In: Proc. 33rd IEEE Symp. Found. Computer Science, pp. 247–256 (1992)

    Google Scholar 

  22. Galil, Z., Park, K.: Alphabet-independent two-dimensional witness computation. Manuscript (1993)

    Google Scholar 

  23. Goldschlager, L.: A unified approach to models of synchronous parallel machines. J. ACM 29, 1073–1086 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  24. Kucera, L.: Parallel computation and conflicts in memory access. Inform. Process. Lett. 14(2), 93–96 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  25. Main, G.M., Lorentz, R.J.: An O(n logn) algorithm for finding all repetitions in a string. J. Algorithms 5, 422–432 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  26. Morse, M., Hedlund, G.A.: Symbolic dynamics II: Sturmian sequences. Amer. J. Math. 61, 1–42 (1940)

    Article  MathSciNet  Google Scholar 

  27. Réveillès, J.-P.: Combinatorial pieces in digital lines and planes. In: Proc. of the SPIE Conference “Vision Geometry IV”, San Diego, CA, vol. 2573, pp. 23–34 (1995)

    Google Scholar 

  28. Thue, A.: Über unendliche Zeichenreihen. Norske Vid. Selsk. I Mat. Natur. Kl. Skr., Christiania (7), 1–22 (1906)

    Google Scholar 

  29. Thue, A.: Über die gegenseitige Lage gleicher Zeichenreihen. Norske Vid. Selsk. I Mat. Natur. Kl. Skr., Christiania (1), 1–67 (1912)

    Google Scholar 

  30. Vishkin, U.: Optimal parallel pattern matching in strings. Information and Control 67, 91–113 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  31. Vishkin, U.: Implementation of simultaneous memory access in models that forbid it. J. Algorithms 4, 45–50 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  32. Vuillon, L.: Local configurations in a discrete plane. Bull. Belgium Math. Soc. 6, 625–636 (1999)

    MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Mathematics Department, SUNY Buffalo State College, Buffalo, NY, 14222, USA

    Valentin E. Brimkov

Authors
  1. Valentin E. Brimkov
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Editor information

Editors and Affiliations

  1. Department of Computer and Information Sciences, State University of New York at Fredonia, 280 Central Ave, 14063, Fredonia, NY, USA

    Reneta P. Barneva

  2. Mathematics Department, SUNY Buffalo State College, 14222, Buffalo, NY, USA

    Valentin E. Brimkov

  3. Department of Mathematics, Brno University of Technology, 616 69, Brno, Czech Republic

    Josef Šlapal

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Brimkov, V.E. (2014). Parallel Algorithms for Combinatorial Pattern Matching. In: Barneva, R.P., Brimkov, V.E., Šlapal, J. (eds) Combinatorial Image Analysis. IWCIA 2014. Lecture Notes in Computer Science, vol 8466. Springer, Cham. https://doi.org/10.1007/978-3-319-07148-0_2

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  • DOI: https://doi.org/10.1007/978-3-319-07148-0_2

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07147-3

  • Online ISBN: 978-3-319-07148-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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