PROPERTIES OF SOME ILP FORMULATIONS OF A CLASS OF PARTITIONING PROBLEMS

We discuss possible integer linear programming formulations of a class of partitioning problems, which includes vertex (and edge) coloring a nd bin packing, and present some basic properties of the associated li near programming relaxations, possibly improved by means of valid ineq ualities. 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 bo und. Our analysis provides a general framework to unify and generalize some results previously presented in the literature, and should be ta ken into account whenever one considers the possibility of using the f ormulations addressed. (C) 1998 Elsevier Science B.V. All rights reser ved.