In the k-partition problem (k-PP), one is given an edge-weighted undirected graph, and one must partition the node set into at most k subsets, in order to minimise (or maximise) the total weight of the edges that have their end-nodes in the same cluster. Various hierarchical variants of this problem have been studied in the context of data mining. We consider a 'two-level' variant that arises in mobile wireless communications. We show that an exact algorithm based on intelligent preprocessing, cutting planes and symmetry-breaking is capable of solving small- and medium-size instances to proven optimality, and providing strong lower bounds for larger instances.
@article{arxiv.1705.08773,
title = {A Two-Level Graph Partitioning Problem Arising in Mobile Wireless Communications},
author = {Jamie Fairbrother and Adam Letchford and Keith Briggs},
journal= {arXiv preprint arXiv:1705.08773},
year = {2017}
}