Abstract
Clustering graphs based on a comparison of the number of links within clusters and the expected value of this quantity in a random graph has gained a lot of attention and popularity in the last decade. Recently, Aldecoa and Marín proposed a related, but slightly different approach leading to the quality measure surprise, and reported good behavior in the context of synthetic and real world benchmarks. We show that the problem of finding a clustering with optimum surprise is \(\mathcal{NP}\)-hard. Moreover, a bicriterial view on the problem permits to compute optimum solutions for small instances by solving a small number of integer linear programs, and leads to a polynomial time algorithm on trees.
This work was partially supported by the DFG under grant WA 654/19-1.
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Fleck, T., Kappes, A., Wagner, D. (2014). Graph Clustering with Surprise: Complexity and Exact Solutions. In: Geffert, V., Preneel, B., Rovan, B., Štuller, J., Tjoa, A.M. (eds) SOFSEM 2014: Theory and Practice of Computer Science. SOFSEM 2014. Lecture Notes in Computer Science, vol 8327. Springer, Cham. https://doi.org/10.1007/978-3-319-04298-5_20
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DOI: https://doi.org/10.1007/978-3-319-04298-5_20
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