The Complexity of Finding a Large Subgraph under Anonymity Constraints

  • Robert Bredereck
  • Sepp Hartung
  • André Nichterlein
  • Gerhard J. Woeginger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8283)


We define and analyze an anonymization problem in undirected graphs, which is motivated by certain privacy issues in social networks. The goal is to remove a small number of vertices from the graph such that in the resulting subgraph every occurring vertex degree occurs many times.

We prove that the problem is NP-hard for trees, and also for a number of other highly structured graph classes. Furthermore we provide polynomial time algorithms for other graph classes (like threshold graphs), and thereby establish a sharp borderline between hard and easy cases of the problem. Finally we perform a parametrized analysis, and we concisely characterize combinations of natural parameters that allow FPT algorithms.


Maximum Degree Vertex Cover Graph Class Perfect Graph Split Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Robert Bredereck
    • 1
  • Sepp Hartung
    • 1
  • André Nichterlein
    • 1
  • Gerhard J. Woeginger
    • 2
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany
  2. 2.Department of Mathematics and Computer ScienceTU EindhovenThe Netherlands

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