Reconstructing Binary Matrices with Neighborhood Constraints: An NP-hard Problem
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.
KeywordsDiscrete Tomography polynomial time reduction NP- complete Problem
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