On the relative strength of split, triangle and quadrilateral cuts
Integer programs defined by two equations with two free integer variables and nonnegative continuous variables have three
types of nontrivial facets: split, triangle or quadrilateral inequalities. In this paper, we compare the strength of these
three families of inequalities. In particular we study how well each family approximates the integer hull. We show that, in
a well defined sense, triangle inequalities provide a good approximation of the integer hull. The same statement holds for
quadrilateral inequalities. On the other hand, the approximation produced by split inequalities may be arbitrarily bad.