José Neto

A constraint generation algorithm for large scale linear programs using multiple-points separation

In order to solve linear programs with a large number of constraints, constraint generation techniques are often used. In these algorithms, a relaxation of the formulation containing only a subset of the constraints is first solved. Then a separation procedure is called which adds to the relaxation any inequality of the formulation that is violated by the current solution. The process is iterated until no violated inequality can be found. In this paper, we present a separation procedure that uses several points to generate violated constraints. The complexity of this separation procedure and of some related problems is studied. Also, preliminary computational results about the advantages of using multiple-points separation procedures over traditional separation procedures are given for random linear programs and survivable network design. They illustrate that, for some specific families of linear programs, multiple-points separation can be computationally effective.

On the Most Imbalanced Orientation of a Graph

We study the problem of orienting the edges of a graph such that the minimum over all the vertices of the absolute difference between the outdegree and the indegree of a vertex is maximized. We call this minimum the imbalance of the orientation, i.e. the higher it gets, the more imbalanced the orientation is. We study this problem denoted by MaxIm. We first present different characterizations of the graphs for which the optimal objective value of MaxIm is zero. Next we show that it is generally NP-complete and cannot be approximated within a ratio of \(\frac{1}{2}+\varepsilon \) for any constant \(\varepsilon >0\) in polynomial time unless \(\mathtt P =\mathtt NP \) even if the minimum degree of the graph \(\delta \) equals 2. Finally we describe a polynomial-time approximation algorithm whose ratio is equal to \(\frac{1}{2}\) for graphs where \(\delta \equiv 0[4]\) or \(\delta \equiv 1[4]\) and \((\frac{1}{2}-\frac{1}{\delta })\) for general graphs.

On the most imbalanced orientation of a graph

We study the problem of orienting the edges of a graph such that the minimum over all the vertices of the absolute difference between the outdegree and the indegree of a vertex is maximized. We call this minimum the imbalance of the orientation, i.e. the higher it gets, the more imbalanced the orientation is. The studied problem is denoted by

A Polyhedral View to Generalized Multiple Domination and Limited Packing

{{\mathrm{\textsc {MaxIm}}}}

On the diameter of cut polytopes

MAXIM. We first characterize graphs for which the optimal objective value of

Acceleration of cutting-plane and column generation algorithms: Applications to network design

{{\mathrm{\textsc {MaxIm}}}}