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. © 2008 Springer Berlin Heidelberg.
CITATION STYLE
Masilamani, V., Krithivasan, K., Subramanian, K. G., & Huey, A. M. (2008). Efficient algorithms for reconstruction of 2d-arrays from extended parikh images. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5359 LNCS, pp. 1137–1146). https://doi.org/10.1007/978-3-540-89646-3_113
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