A Two-Level Graph Partitioning Problem Arising in Mobile Wireless Communications

TL;DR

This paper introduces a two-level graph partitioning problem relevant to mobile wireless communications and presents an exact algorithm that efficiently solves small to medium instances, offering strong bounds for larger cases.

Contribution

It formulates a new two-level partitioning problem specific to wireless communications and develops an exact solution method with preprocessing, cutting planes, and symmetry-breaking techniques.

Findings

Exact algorithm solves small and medium instances optimally.

Provides strong lower bounds for larger instances.

Demonstrates effectiveness in the context of wireless communications.

Abstract

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.