Clique facets of the axial and planar assignment polytopes

The (k,s) assignment problem sets a unified framework for studying the facial structure of families of assignment polytopes. Through this framework, we derive classes of clique facets for all axial and planar assignment polytopes. For each of these classes, a polynomial-time separation procedure is described. Furthermore, we provide computational experience illustrating the efficiency of these facet-defining inequalities when applied as cutting planes.