Properties of some ILP formulations of a class of partitioning problems Original Research Article

We discuss possible integer linear programming formulations of a class of partitioning problems, which includes vertex (and edge) coloring and bin packing, and present some basic properties of the associated linear programming relaxations, possibly improved by means of valid inequalities. In particular, we show that these relaxations are sometimes easily solved without resorting to an LP solver, and derive the worst-case performance of the associated bound on the optimal solution value. We also show which is the contribution of each inequality to this bound. Our analysis provides a general framework to unify and generalize some results previously presented in the literature, and should be taken into account whenever one considers the possibility of using the formulations addressed.