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Efficient Algorithms for Reconstruction of 2D-Arrays from Extended Parikh Images

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Advances in Visual Computing (ISVC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5359))

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Abstract

The concept of a Parikh matrix or an extended Parikh mapping of words introduced by Mateescu et al (2001) is formulated here for two-dimensional (2D) arrays. A polynomial time algorithm is proposed to reconstruct an unknown 2D-array over { 0,1 } from its image under the extended Parikh mapping along a single direction. On the other hand the problem of reconstructing a 2D-array over { 0,1 } from its image under the extended Parikh mapping along three or more directions is shown to be NP-hard. Also a polynomial time algorithm to reconstruct a 2D-array over {0,1} with a maximum number of ones close to the main diagonal of the array is presented by reducing the problem to Min-cost Max-flow problem.

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References

  1. Mateescu, A., Salomaa, A., Salomaa, K., Yu, S.: A sharpening of the Parikh mapping. Theoret. Informatics Appl. 35, 551–564 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. Batenberg, K.J.: Advances in discrete tomography and its applications. In: Network flow algorithms for discrete tomography. Birkhauser, Basel (2007)

    Chapter  Google Scholar 

  3. Batenberg, K.J.: An evolutionary algorithm for discrete tomography. Discrete Applied Mathematics 151, 36–54 (2005)

    Article  MathSciNet  Google Scholar 

  4. Gardner, R.J., Gritzmann, P.: On the computational complexity of reconstruction lattice sets from their X-rays. Discrete Mathematics 202, 45–71 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  5. Herman, G.T., Kuba, A. (eds.): DISCRETE TOMOGRAPHY Foundations, Algorithms and Applications. Birkhauser, Basel (1999)

    MATH  Google Scholar 

  6. Ryser, H.J.: Combinatorial properties of matrices of zeroes and ones. Canad. J. Math. 9, 371–377 (1957)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, 600 036, India

    V. Masilamani & Kamala Krithivasan

  2. School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia

    K. G. Subramanian & Ang Miin Huey

Authors
  1. V. Masilamani
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  2. Kamala Krithivasan
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  3. K. G. Subramanian
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  4. Ang Miin Huey
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Nevada, Reno, USA

    George Bebis

  2. NASA Ames Research Center, Moffett Field, CA, USA

    Richard Boyle

  3. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Bahram Parvin

  4. Desert Research Institute, Reno, NV, USA

    Darko Koracin

  5. Digital Image Research Center, Kingston University, London, UK

    Paolo Remagnino

  6. Mitsubishi Electric Research Laboratories, P.O. Box 02139, Cambridge, MA, USA

    Fatih Porikli

  7. Computer and Information Science and Engineering, University of Florida, P.O. Box, FL 32611-6120, Gainsville, USA

    Jörg Peters

  8. IBM T.J. Watson Research Center, 19 Skyline Drive, NY 10532, Hawthorne, USA

    James Klosowski

  9. 128 Memorial Mall, Stewart B001, IN 47907, West Lafayette, USA

    Laura Arns

  10. Denver Museum of Nature and Space, 2001 Colorade Blvd. Denver,, CO 80205, USA

    Yu Ka Chun

  11. Departmen of Computer Science,, NC State University, Campus Box 8206, NC 27695-8206, Raleigh, USA

    Theresa-Marie Rhyne

  12. Los Alamos National Labs, P.O. Box 1663, NM 87545, Los Alamos, USA

    Laura Monroe

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© 2008 Springer-Verlag Berlin Heidelberg

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Masilamani, V., Krithivasan, K., Subramanian, K.G., Huey, A.M. (2008). Efficient Algorithms for Reconstruction of 2D-Arrays from Extended Parikh Images. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2008. Lecture Notes in Computer Science, vol 5359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89646-3_113

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  • DOI: https://doi.org/10.1007/978-3-540-89646-3_113

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89645-6

  • Online ISBN: 978-3-540-89646-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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