The complexity of degree anonymization by vertex addition

Robert Bredereck, Vincent Froese, Sepp Hartung, André Nichterlein, Rolf Niedermeier, Nimrod Talmon

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Motivated by applications in privacy-preserving data publishing, we study the problem of making an undirected graph k-anonymous by adding few vertices (together with some incident edges). That is, after adding these "dummy vertices", for every vertex degree d appearing in the resulting graph, there shall be at least k vertices with degree d. We explore three variants of vertex addition (justified by real-world considerations) and study their (parameterized) computational complexity. We derive mostly intractability results, even for very restricted cases (including trees and bounded-degree graphs) but also obtain some encouraging fixed-parameter tractability results.

Original languageEnglish
Pages (from-to)16-34
Number of pages19
JournalTheoretical Computer Science
StatePublished - 23 Nov 2015
Externally publishedYes


  • Degree-constrained editing
  • Fixed-parameter tractability
  • Graph modification
  • Kernelization
  • NP-hardness
  • Parameterized complexity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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