Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study a mixed integer linear program with m integer variables and k nonnegative continuous variables in the form of the relaxation of the corner polyhedron that was introduced by Andersen, Louveaux, ismantel and Wolsey [Inequalities from two rows of a simplex tableau, Proc. IPCO 2007, LNCS, vol. 4513, Springer, pp. 1{15].  describe the facets of this mixed integer linear program via the extreme points of a ll-dened polyhedron.  then utilize this description to give polynomial time algorithms to derive valid inequalities with optimal lp norm for arbitrary, but xed m. For the case of m = 2,  give a renement and a new proof of a characterization of the facets by Cornu ejols and Margot [ On the facets of mixed integer programs with two integer variables and two constraints, Math. Programming 120 (2009), 429{456]. The key point of our approach is that the conditions are much more explicit and can be tested in a more direct manner, removing the need for a reduction algorithm. These results allow us to show that the relaxed corner polyhedron has only polynomially many facets.
['Amitabh Basu', 'Robert Hildebrand', 'Matthias Köppe']
I am writing a research paper on a idea Algorithmic and Complexity Results for Cutting Planes Derived from Maximal Lattice-Free Convex Sets
[{"from": "human", "value": "I am writing a research paper on a idea Algorithmic and Complexity Results for Cutting Planes Derived from Maximal Lattice-Free Convex Sets"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study a mixed integer linear program with m integer variables and k nonnegative continuous variables in the form of the relaxation of the corner polyhedron that was introduced by Andersen, Louveaux, ismantel and Wolsey [Inequalities from two rows of a simplex tableau, Proc. IPCO 2007, LNCS, vol. 4513, Springer, pp. 1{15].  describe the facets of this mixed integer linear program via the extreme points of a ll-dened polyhedron.  then utilize this description to give polynomial time algorithms to derive valid inequalities with optimal lp norm for arbitrary, but xed m. For the case of m = 2,  give a renement and a new proof of a characterization of the facets by Cornu ejols and Margot [ On the facets of mixed integer programs with two integer variables and two constraints, Math. Programming 120 (2009), 429{456]. The key point of our approach is that the conditions are much more explicit and can be tested in a more direct manner, removing the need for a reduction algorithm. These results allow us to show that the relaxed corner polyhedron has only polynomially many facets."}]