Abstract
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 incident edges). That is, after adding these “dummy vertices”, for every vertex degree d 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 (worst-case) intractability results, even for very restricted cases (including trees or bounded-degree graphs) but also obtain a few encouraging fixed-parameter tractability results.
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
Bredereck, R., Hartung, S., Nichterlein, A., Woeginger, G.J.: The complexity of finding a large subgraph under anonymity constraints. In: Cai, L., Cheng, S.-W., Lam, T.-W. (eds.) Algorithms and Computation. LNCS, vol. 8283, pp. 152–162. Springer, Heidelberg (2013)
Casas-Roma, J., Herrera-Joancomartí, J., Torra, V.: An algorithm for k-degree anonymity on large networks. In: Proc. ASONAM 2013, pp. 671–675. ACM Press (2013)
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. Social Netw. Analys. Mining 3(3), 381–399 (2013)
Chester, S., Kapron, B.M., Srivastava, G., Venkatesh, S.: Complexity of social network anonymization. Social Netw. Analys. Mining 3(2), 151–166 (2013)
Clarkson, K.L., Liu, K., Terzi, E.: Towards identity anonymization in social networks. In: Link Mining: Models, Algorithms, and Applications, pp. 359–385. Springer (2010)
Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity. Springer (2013)
Erdős, P., Kelly, P.: The minimal regular graph containing a given graph. Amer. Math. Monthly 70, 1074–1075 (1963)
Fellows, M.R., Jansen, B.M.P., Rosamond, F.A.: Towards fully multivariate algorithmics: Parameter ecology and the deconstruction of computational complexity. Eur. J. Combin. 34(3), 541–566 (2013)
Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer (2006)
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); To appear in Information and Computation
Lenstra, H.W.: Integer programming with a fixed number of variables. Math. Oper. Res. 8, 538–548 (1983)
Liu, K., Terzi, E.: Towards identity anonymization on graphs. In: ACM SIGMOD Conference, SIGMOD 2008, pp. 93–106. ACM (2008)
Lovász, L., Plummer, M.D.: Matching Theory. Annals of Discrete Mathematics, vol. 29. North-Holland (1986)
Lu, X., Song, Y., Bressan, S.: Fast identity anonymization on graphs. In: Liddle, S.W., Schewe, K.-D., Tjoa, A.M., Zhou, X. (eds.) DEXA 2012, Part I. LNCS, vol. 7446, pp. 281–295. Springer, Heidelberg (2012)
Lueker, G.S.: Two NP-complete problems in nonnegative integer programming. Technical report. Computer Science Laboratory, Princeton University (1975)
Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)
Niedermeier, R.: Reflections on multivariate algorithmics and problem parameterization. In: Proc. 27th STACS. LIPIcs, vol. 5, pp. 17–32. Schloss Dagstuhl–Leibniz-Zentrum für Informatik (2010)
Zhou, B., Pei, J.: The k-anonymity and l-diversity approaches for privacy preservation in social networks against neighborhood attacks. Knowl. Inf. Syst. 28(1), 47–77 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Bredereck, R., Froese, V., Hartung, S., Nichterlein, A., Niedermeier, R., Talmon, N. (2014). The Complexity of Degree Anonymization by Vertex Addition. In: Gu, Q., Hell, P., Yang, B. (eds) Algorithmic Aspects in Information and Management. AAIM 2014. Lecture Notes in Computer Science, vol 8546. Springer, Cham. https://doi.org/10.1007/978-3-319-07956-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-07956-1_5
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07955-4
Online ISBN: 978-3-319-07956-1
eBook Packages: Computer ScienceComputer Science (R0)