The k-partition problem is an NP-hard combinatorial optimisation problem with many applications. Chopra and Rao introduced two integer programming formulations of this problem, one having both node and edge variables, and the other having only edge variables. We show that, if we take the polytopes associated with the `edge-only' formulation, and project them into a suitable subspace, we obtain the polytopes associated with the `node-and-edge' formulation. This result enables us to derive new valid inequalities, new separation algorithms, and a new semidefinite programming relaxation.
Citation
J. Fairbrother & A.N. Letchford (2017) Projection results for the k-partition problem. Discrete Optimization, 26, 97-111.