A refined complexity analysis of degree anonymization in graphs

Authors:
Sepp Hartung;André Nichterlein;Rolf Niedermeier;Ondřej Suchý
Affiliations:
Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Germany;Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Germany;Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Germany;Faculty of Information Technology, Czech Technical University in Prague, Czech Republic
Venue:
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
Year:
2013

Citing 18
Cited 0

The asymmetric median tree—a new model for building consensus trees

Discrete Applied Mathematics - Special volume on computational molecular biology
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
An efficient reduction technique for degree-constrained subgraph and bidirected network flow problems

STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)

Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Invitation to data reduction and problem kernelization

ACM SIGACT News
Planetary-scale views on a large instant-messaging network

Proceedings of the 17th international conference on World Wide Web
Towards identity anonymization on graphs

Proceedings of the 2008 ACM SIGMOD international conference on Management of data
De-anonymizing Social Networks

SP '09 Proceedings of the 2009 30th IEEE Symposium on Security and Privacy
Kernelization: New Upper and Lower Bound Techniques

Parameterized and Exact Computation
Privacy-preserving data publishing: A survey of recent developments

ACM Computing Surveys (CSUR)
Achieving anonymity via clustering

ACM Transactions on Algorithms (TALG)
Heuristic algorithms in computational molecular biology

Journal of Computer and System Sciences
The k-anonymity and l-diversity approaches for privacy preservation in social networks against neighborhood attacks

Knowledge and Information Systems
Sharing graphs using differentially private graph models

Proceedings of the 2011 ACM SIGCOMM conference on Internet measurement conference
Editing graphs to satisfy degree constraints: A parameterized approach

Journal of Computer and System Sciences
On the Hardness of Graph Anonymization

ICDM '11 Proceedings of the 2011 IEEE 11th International Conference on Data Mining
Anonymizing Subsets of Social Networks with Degree Constrained Subgraphs

ASONAM '12 Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012)
Parameterized Complexity

Parameterized Complexity

Quantified Score

Hi-index	0.00

Visualization

Abstract

Motivated by a strongly growing interest in graph anonymization in the data mining and databases communities, we study the NP-hard problem of making a graph k-anonymous by adding as few edges as possible. Herein, a graph is k-anonymous if for every vertex in the graph there are at least k−1 other vertices of the same degree. Our algorithmic results shed light on the performance quality of a popular heuristic due to Liu and Terzi [ACM SIGMOD 2008]; in particular, we show that the heuristic provides optimal solutions in case that many edges need to be added. Based on this, we develop a polynomial-time data reduction, yielding a polynomial-size problem kernel for the problem parameterized by the maximum vertex degree. This result is in a sense tight since we also show that the problem is already NP-hard for H-index three, implying NP-hardness for smaller parameters such as average degree and degeneracy.