New bounds and constraint propagation techniques for the clique partitioning problem

Authors:
Florian Jaehn;Erwin Pesch
Affiliations:
Chair of Sustainable Operations and Logistics, University Augsburg, 86159 Augsburg, Germany;Institute of Information Systems, University Siegen, 57068 Siegen, Germany
Venue:
Discrete Applied Mathematics
Year:
2013

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Abstract

This paper considers the problem of clustering the vertices of a complete edge-weighted graph. The objective is to maximize the sum of the edge weights within the clusters (also called cliques). This so-called Clique Partitioning Problem (CPP) is NP-complete, and has several real-life applications such as groupings in flexible manufacturing systems, in biology, in flight gate assignment, etc. Numerous heuristics and exact approaches as well as benchmark tests have been presented in the literature. Most exact methods use branch and bound with branching over edges. We present tighter upper bounds for each search tree node than those known from the literature, improve the constraint propagation techniques for fixing edges in each node, and present a new branching scheme. The theoretical improvements are reflected by computational tests with real-life data. Although a standard solver delivers best results on randomly generated data, the runtime of the proposed algorithm is very low when being applied to instances on object clustering.