The complexity of degree anonymization by graph contractions

Nimrod Talmon, Sepp Hartung

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 the computational complexity of degree anonymization by graph contractions. We consider 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 NP-hard even for some very restricted inputs, and identify some fixed-parameter tractable cases.

Original languageEnglish
Pages (from-to)212-225
Number of pages14
JournalInformation and Computation
StatePublished - 1 Oct 2017
Externally publishedYes


  • Computational complexity
  • Data publishing
  • Degree-constrained editing
  • Fixed-parameter tractability
  • Graph modifications
  • Parameterized complexity
  • Privacy

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics


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