The Complexity of Finding a Large Subgraph under Anonymity Constraints
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.
KeywordsMaximum Degree Vertex Cover Graph Class Perfect Graph Split Graph
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- 2.Brandstädt, A., Le, V.B., Spinrad, J.P.: Graph Classes: a Survey. SIAM Monographs on Discrete Mathematics and Applications, vol. 3. SIAM (1999)Google Scholar
- 3.Chester, S., Kapron, B., Srivastava, G., Venkatesh, S.: Complexity of social network anonymization. Social Network Analysis and Mining, 1–16 (2012a)Google Scholar
- 4.Chester, S., Kapron, B.M., Ramesh, G., Srivastava, G., Thomo, A., Venkatesh, S.: Why Waldo befriended the dummy? k-anonymization of social networks with pseudo-nodes. In: Social Network Analysis and Mining, pp. 1–19 (2012b) ISSN 1869-5450Google Scholar
- 7.Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer (1999)Google Scholar
- 8.Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman (1979)Google Scholar
- 9.Golumbic, M.C.: Algorithmic graph theory and perfect graphs, 2nd edn. Annals of Discrete Mathematics, vol. 57. Elsevier B.V. (2004), 1st edn. Academic Press (1980)Google Scholar
- 11.Liu, K., Terzi, E.: Towards identity anonymization on graphs. In: Proc. ACM SIGMOD International Conference on Management of Data, SIGMOD 2008, pp. 93–106. ACM (2008)Google Scholar
- 13.Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)Google Scholar
- 14.Vazirani, V.V.: Approximation Algorithms. Springer (2001)Google Scholar
- 15.Wu, X., Ying, X., Liu, K., Chen, L.: A survey of privacy-preservation of graphs and social networks. In: Managing and Mining Graph Data, pp. 421–453. Springer (2010)Google Scholar