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

Authors:
V. Masilamani;Kamala Krithivasan;K. G. Subramanian;Ang Miin Huey
Affiliations:
Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, India 600 036;Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, India 600 036;School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia 11800;School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia 11800
Venue:
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
Year:
2008

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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.