On the polyhedron of the K-partitioning problem with representative variables

The K-partitioning problem consists of partitioning the vertices of a graph in K sets so as to minimize a function of the edge weights. We introduce a linear mixed integer formulation with edge variables and representative variables. We consider the corresponding polyhedron and show which inequalities are facet-defining. We study several families of facet-defining inequalities and provide experimental results showing that they improve significantly the linear relaxation of our formulation.