| Abstract |
: |
In this note, we present a simple geometric argument to determine a lower bound on the split
rank of intersection cuts. As a first step of this argument, a polyhedral subset of the latticefree
convex set that is used to generate the intersection cut is constructed. We call this subset
the restricted lattice-free set. It is then shown that [log2(l)] is a lower bound on the split rank
of the intersection cut, where l is the number of integer points lying on the boundary of the
restricted lattice-free set satisfying the condition that no two points lie on the same facet of the restricted lattice-free set. The use of this result is illustrated to obtain a lower bound of [log2(n +1)] on the split rank of n-row mixing inequalities. |
