The   K     K       -partitioning problem consists in partitioning the vertices of a weighted graph in   K     K        sets in order to minimize a function related to the edge weights. We introduce a linear mixed integer formulation with edge variables and representative variables. We investigate the polyhedral combinatorics of the problem, study several families of facet-defining inequalities and evaluate their efficiency on the linear relaxation.
['Zacharie Ales', 'Arnaud Knippel', 'Alexandre Pauchet']
Polyhedral combinatorics of the K-partitioning problem with representative variables