Reconstructing a matrix with a given list of coefficients and prescribed row and column sums is NP-hard

Abstract

We investigate a natural generalization of the problem of reconstruction of a binary matrix A with prescribed row and column sums: we consider an integer matrix whose list of coefficients is given in the input. The question is to organize the coefficients in the matrix in order to obtain prescribed row and column sums. We prove that this problem is NP-complete by reducing it to a 2D problem of Discrete Tomography with 3 directions of projections. © 2008 Springer-Verlag Berlin Heidelberg.