Optimization and reconstruction of hv-convex (0,1)-matrices

We consider a variant of the NP-hard problem of reconstructing hv-convex (0,1)-matrices from known row and column sums. Instead of requiring the ones to occur consecutively in each row and column, we maximize the number of neighboring ones. This is reformulated as an integer programming problem. A solution method based on variable splitting is proposed and tested with good results on moderately sized test problems.