A useful characterization of the feasible region of binary linear programs

In view of providing an explicit representation of the convex hull by listing all the facets, it is interesting to describe the integral feasible region in terms of interior points, i.e. hypercube vertices which are feasible in (1) and such that all their adjacent hypercube vertices are also feasible in (1) and exterior points, for which there is at least one infeasible adjacent hypercube vertex. Whereas interior points belong to trivial facets of the convex hull (i.e. those facets which are also hypercube facets), exterior points define all the non-trivial facets. In this work we use a particular type of rounding along the hypercube edges (called flattening) to derive all exterior points of the feasible region of BLPs. We also show how to exploit this characterization to derive practically useful valid inequalities passing through hypercube vertices, and their relation to Balas’ intersection cuts [1]. Other works in the literature which are closely related to this topic are geometric [3] and canonical [2] cuts; both of these also pass through hypercube vertices, and therefore also identify exterior points.