From Totally Unimodular to Balanced 0, ±1 Matrices: A Family of Integer Polytopes

In this paper we introduce a family of integer polytopes and characterize them in terms of forbidden submatrices. The two extreme cases in this family arise when the constraint matrix is totally unimodular and balanced, respectively. This generalizes results of Truemper-Chandrasekaran and Conforti-Cornuejols.