EURO Journal on Computational Optimization

, Volume 3, Issue 2, pp 111–129

Evaluating the quality of image matrices in blockmodeling

Original Paper

DOI: 10.1007/s13675-015-0034-y

Cite this article as:
Wiesberg, S. & Reinelt, G. EURO J Comput Optim (2015) 3: 111. doi:10.1007/s13675-015-0034-y
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Abstract

One approach for analyzing large networks is to partition its nodes into classes where the nodes in a class have similar characteristics with respect to their connections in the network. A class is represented as a blockmodel (or image matrix). In this context, a specific question is to test whether a presumed blockmodel is well reflected in the network or to select from a choice of possible blockmodels the one fitting best. In this paper, we formulate these problems as combinatorial optimization problems. We show that the evaluation of a blockmodel’s quality is a generalization of well-known optimization problems such as quadratic assignment, minimum \(k\)-cut, traveling salesman, and minimum edge cover. A quadratic integer programming formulation is derived and linearized by making use of properties of these special cases. With a branch-and-cut approach, the resulting formulation is solved up to 10,000 times faster than a comparable formulation from the literature.

Keywords

Regular equivalence Blockmodeling Quadratic integer programming Linearization techniques 

Mathematics Subject Classification

80-08 90C11 90B10 05C82 

Copyright information

© EURO - The Association of European Operational Research Societies 2015

Authors and Affiliations

  1. 1.Institut für InformatikUniversität HeidelbergHeidelbergGermany

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