Row family inequalities for the set covering polyhedron

Generalized minor inequalities for the set covering polyhedron related to circulant matrices

“…For instance, similarly to generalized minor inequalities, clique family inequalities have only two different coefficients, which are consecutive integers. First steps in this direction have been undertaken in [3,4].…”

“…Finally, sinceb T ∈ Z n , 0 ≤ y < 1, and 0 ≤ z < 1, we must have y = (1− r k ′ )1, z = 0, and henceb T = ((r+1)1 T , r1 T , r1 T ) = r1 T + j∈W (e j ) T . Then the statement of the theorem follows from (4).…”

On dominating set polyhedra of circular interval graphs

“…The class of row family inequalities (rfi) was proposed in [3] as a counterpart to clique family inequalities in the set packing case [25]. We describe them at next, slightly modified to fit in our current notation.…”

On the Chvátal-rank of facets for the set covering polyhedron of circular matrices

“…The boolean facets include the inequalities x ≥ 0 and Ax ≥ 1 defining Q(A) which can be considered as the inequalities corresponding to (i) and (ii) for the set covering polyhedron. More recently, the class of row family inequalities was proposed in [3] as a counterpart of clique family inequalities in the set covering case. In fact, the same ideas used for P * (A) can be extended to show that Q * (A) is completely described by boolean facets and a particular subclass of row family inequalities associated with certain minors [5].…”

“…The Chvátal-rank of Q(A) has been addressed in several previous works. Any minor inequality has Chvátal-depth at most one, but it has been observed in [3] that this might not be the case for row family inequalities.…”