A Two-Level Graph Partitioning Problem Arising in Mobile 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2017
- DOI:
- 10.48550/arXiv.1705.08773
- arXiv:
- arXiv:1705.08773
- Bibcode:
- 2017arXiv170508773F
- Keywords:
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- Mathematics - Optimization and Control;
- Computer Science - Data Structures and Algorithms;
- Mathematics - Combinatorics