Reconstruction of discrete sets with absorption Original Research Article

The uniqueness problem is considered when binary matrices are to be reconstructed from their absorbed row and column sums. Let the absorption coefficient μ be selected such that image . Then it is proved that if a binary matrix is non-uniquely determined, then it contains a special pattern of 0s and 1s called composition of alternatively corner-connected components. In a previous paper [Discrete Appl. Math. (submitted)] we proved that this condition is also sufficient, i.e., the existence of such a pattern in the binary matrix is necessary and sufficient for its non-uniqueness.