4 citations · 6 across the 8 of their papers we have counts for
11 papers
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 red-blue-yellow matching problem
Manuel Aprile, Marco Di Summa
We consider the red-blue-yellow matching problem: given two natural numbers , and a graph whose edges are colored red, blue or yellow, the goal is to find a matching…
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…
Towards Lower Bounds on the Depth of ReLU Neural Networks
Christoph Hertrich, Amitabh Basu, Marco Di Summa +1
We contribute to a better understanding of the class of functions that can be represented by a neural network with ReLU activations and a given architecture. Using techniques from…
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…
On largest volume simplices and sub-determinants
Marco Di Summa, Friedrich Eisenbrand, Yuri Faenza +1
We show that the problem of finding the simplex of largest volume in the convex hull of points in can be approximated with a factor of in polyn…
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…
On sub-determinants and the diameter of polyhedra
Nicolas Bonifas, Marco Di Summa, Friedrich Eisenbrand +2
We derive a new upper bound on the diameter of a polyhedron P = {x \in R^n : Ax <= b}, where A \in Z^{m\timesn}. The bound is polynomial in n and the largest absolute value of a su…