Abstract
We study the computational complexity of \(k\)-anonymizing a given graph by as few graph contractions as possible. A graph is said to be \(k\)-anonymous if for every vertex in it, there are at least \(k-1\) other vertices with exactly the same degree. The general degree anonymization problem is motivated by applications in privacy-preserving data publishing, and was studied to some extent for various graph operations (most notable operations being edge addition, edge deletion, vertex addition, and vertex deletion). We complement this line of research by studying several variants of graph contractions, which are operations of interest, for example, in the contexts of social networks and clustering algorithms. We show that the problem of degree anonymization by graph contractions is \({\mathsf {NP}}\)-hard even for some very restricted inputs, and identify some fixed-parameter tractable cases.
A full version is available at http://fpt.akt.tu-berlin.de/talmon/abcfv.pdf.
N. Talmon—Supported by DFG Research Training Group MDS (GRK 1408).
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Hartung, S., Talmon, N. (2015). The Complexity of Degree Anonymization by Graph Contractions. In: Jain, R., Jain, S., Stephan, F. (eds) Theory and Applications of Models of Computation. TAMC 2015. Lecture Notes in Computer Science(), vol 9076. Springer, Cham. https://doi.org/10.1007/978-3-319-17142-5_23
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