4 papers
Enumerating integer points in polytopes with bounded subdeterminants
Hongyi Jiang, Amitabh Basu
We show that one can enumerate the vertices of the convex hull of integer points in polytopes whose constraint matrices have bounded and nonzero subdeterminants, in time polynomial…
Complexity of branch-and-bound and cutting planes in mixed-integer optimization -- II
Amitabh Basu, Michele Conforti, Marco Di Summa +1
We study the complexity of cutting planes and branching schemes from a theoretical point of view. We give some rigorous underpinnings to the empirically observed phenomenon that co…
Complexity of branch-and-bound and cutting planes in mixed-integer optimization
Amitabh Basu, Michele Conforti, Marco Di Summa +1
We investigate the theoretical complexity of branch-and-bound (BB) and cutting plane (CP) algorithms for mixed-integer optimization. In particular, we study the relative efficiency…
Split cuts in the plane
Amitabh Basu, Michele Conforti, Marco Di Summa +1
We provide a polynomial time cutting plane algorithm based on split cuts to solve integer programs in the plane. We also prove that the split closure of a polyhedron in the plane h…