Abstract
This paper deals with the reconstruction of binary matrices having exactly − 1 − 4 − adjacency constraints from the horizontal and vertical projections. Such a problem is shown to be non polynomial by means of a reduction which involves the classic NP-complete problem 3-color. The result is reached by bijectively mapping all the four different cells involved in 3-color into maximal configurations of 0s and 1s which show the adjacency constraint, and which can be merged into a single binary matrix.
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Frosini, A., Picouleau, C., Rinaldi, S. (2008). Reconstructing Binary Matrices with Neighborhood Constraints: An NP-hard Problem. In: Coeurjolly, D., Sivignon, I., Tougne, L., Dupont, F. (eds) Discrete Geometry for Computer Imagery. DGCI 2008. Lecture Notes in Computer Science, vol 4992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79126-3_35
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DOI: https://doi.org/10.1007/978-3-540-79126-3_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79125-6
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