Marco Di Summa

Branch and cut algorithms for detecting critical nodes in undirected graphs

In this paper we deal with the critical node problem, where a given number of nodes has to be removed from an undirected graph in order to maximize the disconnections between the node pairs of the graph. We propose an integer linear programming model with a non-polynomial number of constraints but whose linear relaxation can be solved in polynomial time. We derive different valid inequalities and some theoretical results about them. We also propose an alternative model based on a quadratic reformulation of the problem. Finally, we perform many computational experiments and analyze the corresponding results.

Identifying critical nodes in undirected graphs: Complexity results and polynomial algorithms for the case of bounded treewidth

We consider the problem of deleting a limited number of nodes from a graph in order to minimize a connectivity measure of the surviving nodes. We prove that the problem isNP-complete even on quite particular types of graphs, and define a dynamic programming recursion that solves the problem in polynomial time when the graph has bounded treewidth. We extend this polynomial algorithm to several variants of the problem.

On Sub-determinants and the Diameter of Polyhedra

We derive a new upper bound on the diameter of a polyhedron

The mixing set with divisible capacities

P = \{x {\in } {\mathbb {R}}^n :Ax\le b\}

Minimally Infeasible Set-Partitioning Problems with Balanced Constraints

P={x∈Rn:Ax≤b}, where

Extreme Functions with an Arbitrary Number of Slopes

A \in {\mathbb {Z}}^{m\times n}