Geometric characterization of TDI faceted systems

Find a geometric characterization of when a faceted system of linear inequalities is totally dual integral (TDI).

Background

The paper establishes a geometric characterization of TDI for full-dimensional non-degenerate systems: TDI is equivalent to resiliency, and for faceted systems resiliency can be described by integrality after shifting each facet-supporting hyperplane inward to the next integer lattice point.

The authors nevertheless pose the unresolved problem of obtaining a geometric characterization for faceted systems in general, without restricting to the non-degenerate setting.