Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barabási, A., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509 (1999)
Brandstädt, A., Le, V.B., Spinrad, J.P.: Graph Classes: a Survey. SIAM Monographs on Discrete Mathematics and Applications, vol. 3. SIAM (1999)
Chester, S., Kapron, B., Srivastava, G., Venkatesh, S.: Complexity of social network anonymization. Social Network Analysis and Mining, 1–16 (2012a)
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 1869-5450
Chvátal, V., Hammer, P.L.: Aggregation of inequalities in integer programming. Annals of Discrete Mathematics 1, 145–162 (1977)
Dom, M., Lokshtanov, D., Saurabh, S.: Incompressibility through colors and IDs. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part I. LNCS, vol. 5555, pp. 378–389. Springer, Heidelberg (2009)
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer (1999)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman (1979)
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)
Hartung, S., Nichterlein, A., Niedermeier, R., Suchý, O.: A refined complexity analysis of degree anonymization in graphs. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part II. LNCS, vol. 7966, pp. 594–606. Springer, Heidelberg (2013)
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)
Mathieson, L., Szeider, S.: Editing graphs to satisfy degree constraints: A parameterized approach. J. Comput. Syst. Sci. 78(1), 179–191 (2012)
Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)
Vazirani, V.V.: Approximation Algorithms. Springer (2001)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bredereck, R., Hartung, S., Nichterlein, A., Woeginger, G.J. (2013). The Complexity of Finding a Large Subgraph under Anonymity Constraints. In: Cai, L., Cheng, SW., Lam, TW. (eds) Algorithms and Computation. ISAAC 2013. Lecture Notes in Computer Science, vol 8283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45030-3_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-45030-3_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45029-7
Online ISBN: 978-3-642-45030-3
eBook Packages: Computer ScienceComputer Science (R0)