Constrained (0,1)-matrix completion with a staircase of fixed zeros

We study the (0,1)-matrix completion with prescribed row and column sums wherein the ones are permitted in a set of positions that form a Young diagram. We characterize the solvability of such (0,1)-matrix completion problems via the nonnegativity of a structure tensor which is defined in terms of the problem parameters: the row sums, column sums, and the positions of fixed zeros. This reduces the exponential number of inequalities in a direct characterization yielded by the max-flow min-cut theorem to a polynomial number of inequalities. The result is applied to two engineering problems arising in smart grid and real-time systems, respectively.