4 citations · 6 across the 8 of their papers we have counts for
7 papers · 1 filter
Hardness of integer linear feasibility with cyclic support
Marco Di Summa
We prove that integer linear feasibility is strongly -complete even when the constraint matrix has exactly two nonzero entries in every row and column, with its support forming…
The role of rationality in integer-programming relaxations
Manuel Aprile, Gennadiy Averkov, Marco Di Summa +1
For a finite set that can be represented as for some polyhedron , we call a relaxation of and define the relaxation co…
Optimal cutting planes from the group relaxations
Amitabh Basu, Michele Conforti, Marco Di Summa +1
We study quantitative criteria for evaluating the strength of valid inequalities for Gomory and Johnson's finite and infinite group models and we describe the valid inequalities th…
Extreme functions with an arbitrary number of slopes
Amitabh Basu, Michele Conforti, Marco Di Summa +1
For the one dimensional infinite group relaxation, we construct a sequence of extreme valid functions that are piecewise linear and such that for every natural number , th…
The structure of the infinite models in integer programming
Amitabh Basu, Michele Conforti, Marco Di Summa +1
The infinite models in integer programming can be described as the convex hull of some points or as the intersection of halfspaces derived from valid functions. In this paper we st…
Reverse Split Rank
Michele Conforti, Alberto Del Pia, Marco Di Summa +1
The reverse split rank of an integral polyhedron P is defined as the supremum of the split ranks of all rational polyhedra whose integer hull is P. Already in R^3 there exist polyh…
Reverse Chvátal-Gomory rank
Michele Conforti, Alberto Del Pia, Marco Di Summa +2
We introduce the reverse Chvátal-Gomory rank r*(P) of an integral polyhedron P, defined as the supremum of the Chvátal-Gomory ranks of all rational polyhedra whose integer hull is…