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Problems of Reconstructing Words from their Fragments and Applications

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Operations Research and Discrete Analysis

Part of the book series: Mathematics and Its Applications ((MAIA,volume 391))

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Abstract

Problems of reconstructing words from their fragments and applications to image recognition and information theory are considered. A number of new results characterizing the possibilities of recognition and decoding in terms of combinatorial and geometric constructs is presented.

This research was supported by the Russian Foundation for basic Research (Grant 93-01-00449)

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References

  1. C. E. Shannon (1993) Collected Papers, IEEE Press, New York.

    MATH  Google Scholar 

  2. Yu. I. Zhuravlëv (1978) An algebraic approach to the solution of pattern recog nition and identification problems (in Russian), in: Problemy Kibemetiki. Vol. 33, Nauka, Moscow, pp. 5–68

    Google Scholar 

  3. A. P. Gorelik, I. B. Gurevich, and V. A. Skripkin (1985) A Modern State of a Pattern Problem (in Russian), Radio i Svyaz’, Moscow.

    Google Scholar 

  4. M. Lothaire Combinatorics on Words, Encyclopedia of Mathematics and its Applications. Vol.17 Addison-Wesley Publishing Co., Reading, Mass.

    Google Scholar 

  5. A. I. Zenkin and V. K. Leont’ev (1984) A nonclassical pattern recognition problem (in Russian), Zh. Vychisl. Mat i Mat. Fiz. 24, No. 6, 925–931.

    MathSciNet  Google Scholar 

  6. V. K. Leont’ev and Yu. G. Smetanin (1988) Reconstruction of vectors from sets of their fragments (in Russian), Dokl. Akad. Nauk SSSR 302, No. 6, 1319–1322.

    Google Scholar 

  7. V. I. Levenshtein (1991) Perfect codes in the metric of deletion and insertions (in Russian), Diskret Mat 3, No. 1, 3–20.

    MathSciNet  Google Scholar 

  8. B. Manvel, A. Meyerowitz, A. Schwenk, K. Smith, and P. Stockmeyer (1991) Reconstruction of sequences, Discrete Math. 94, No. 3, 209–219.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. A. Evdokimov and V. Nyu (1992) The length of a supersequence for the set of binary words with a given number of units (in Russian), Metody Diskret. Anal. 52, 49–58.

    MathSciNet  Google Scholar 

  10. V. K. Leont’ev (1993) Recognition of binary words from their fragments (in Russian), Dokl. Akad. Nauk 330, No. 4, 434–436.

    MathSciNet  Google Scholar 

  11. V. I. Levenshtein (1965) Binary codes capable of correcting deletions, inser tions, and reversals (in Russian), Dokl. Akad. Nauk SSSR 163, No. 4, 707–710.

    MathSciNet  Google Scholar 

  12. V. V. Kalashnik (1973) Reconstruction of a word from their fragments (in Russian), Vychisl. Mat. i Vychisl. Tekhnika. Vol. 4, Khar’kov, pp. 56–57.

    Google Scholar 

  13. I. Simon (1975) Piecewise testable events. Automata Theory and Formal Languages, pp. 214–222. Lecture Notes in Comput. Sci. Vol. 33, Springer-Verlag, Berlin etc.

    Google Scholar 

  14. V. I. Levenshtein (1974) Elements of coding theory (in Russian), Discrete Mathematics and Mathematical Questions of Cybernetics. Vol. 1, Nauka, Moscow, pp. 207–305.

    Google Scholar 

  15. G. Burosch, U. Frankl, and S. RÖhl (1990) Über Ordnungen von Binäworten, Rostock. Math. Kollog. No. 39, 53–64.

    Google Scholar 

  16. K. Engel and H.-D. Gronau (1985) Sperner Theory in Partially Ordered Sets, BSB B. G. Teubner Verlagsgesellschaft, Leipzig.

    MATH  Google Scholar 

  17. M. R. Garey and D. S. Johnson (1979) Computers and Intractability, Free man, San Francisco.

    MATH  Google Scholar 

  18. D. Maier (1978) The complexity of some problems on subsequences and su persequences, J. Assoc. Comput. Mach. 25, No. 2, 322–336.

    Article  MathSciNet  MATH  Google Scholar 

  19. Sh. M. Aliev (1993) Algorithmic questions for the construction of optimal codes for many receivers (in Russian), Dis. Kand. Fiz.-Mat. Nauk, Moscow.

    Google Scholar 

  20. E. M. Reingold, J. Nievergeld, and N. Deo (1977) Combinatorial Algorithms: Theory and Practice, Prentice-Hall, Inc., Englewood Cliffs, New Jork.

    Google Scholar 

  21. M. Hall, Jr. (1967) Combinatorial Theory, Blaisdell Publishing Company, Waltham, Toronto, and London.

    MATH  Google Scholar 

  22. A. A. Evdokimov (1969) The maximal length of a chain in the u-dimensional unit cube (in Russian), Mat Zametki 6, No. 3, 309–319.

    MathSciNet  Google Scholar 

  23. V. Nyu (1990) Covering of a set of words by chains (in Russian), Dis. Kand. Fiz.-Mat. Nauk, Institute of Mathematics, Novosibirsk.

    Google Scholar 

  24. V. Nyu and A. A. Evdokimov (1983) Covering of graphs by paths (in Russian), Metody Diskret. Anal 40, 72–86.

    MathSciNet  MATH  Google Scholar 

  25. W. T. Tutte (1984) Graph Theory, Addison-Wesley Publishing Company, Reading, Massachusetts.

    MATH  Google Scholar 

  26. Ya. S. Smetanich (1971) The reconstruction of words (in Russian), Dokl. Akad. Nauk SSSR 201, No. 4, 798–800.

    MathSciNet  Google Scholar 

  27. Ya. S. Smetanich (1973) On the reconstruction of words (in Russian), Mathe matical Logic, Theory of Algorithms, and Theory of Sets. Trudy Mat. Inst. Steklov. Vol. 133, Nauka, Moscow, pp. 183–202.

    Google Scholar 

  28. Yu. G. Smetanin (1986) On some problems for the reconstruction of words from their fragments (in Russian), Dis. Kand. Fiz.-Mat. Nauk, Vychisl.

    Google Scholar 

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Authors and Affiliations

  1. Computing Center, ul. Vavilova, 40, Moscow, GSP-1, 117967, Russia

    V. K. Leont’ev

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  1. V. K. Leont’ev
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© 1997 Springer Science+Business Media Dordrecht

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Leont’ev, V.K. (1997). Problems of Reconstructing Words from their Fragments and Applications. In: Operations Research and Discrete Analysis. Mathematics and Its Applications, vol 391. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5678-3_11

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  • DOI: https://doi.org/10.1007/978-94-011-5678-3_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6395-1

  • Online ISBN: 978-94-011-5678-3

  • eBook Packages: Springer Book Archive

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