Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Some APX-completeness results for cubic graphs
Theoretical Computer Science
Approximation algorithms
Protecting Respondents' Identities in Microdata Release
IEEE Transactions on Knowledge and Data Engineering
k-anonymity: a model for protecting privacy
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
On the complexity of optimal K-anonymity
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
\ell -Diversity: Privacy Beyond \kappa -Anonymity
ICDE '06 Proceedings of the 22nd International Conference on Data Engineering
Algorithmic construction of sets for k-restrictions
ACM Transactions on Algorithms (TALG)
Approximate algorithms for K-anonymity
Proceedings of the 2007 ACM SIGMOD international conference on Management of data
k-Anonymization with Minimal Loss of Information
IEEE Transactions on Knowledge and Data Engineering
The hardness and approximation algorithms for l-diversity
Proceedings of the 13th International Conference on Extending Database Technology
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Resolving the complexity of some data privacy problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Parameterized complexity of k-anonymity: hardness and tractability
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Anonymizing binary and small tables is hard to approximate
Journal of Combinatorial Optimization
ICDT'05 Proceedings of the 10th international conference on Database Theory
The l-Diversity problem: Tractability and approximability
Theoretical Computer Science
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The problem of publishing personal data without giving up privacy is becoming increasingly important. Different interesting formalizations have been recently proposed in this context, i.e. k-anonymity [17,18] and l-diversity [12]. These approaches require that the rows in a table are clustered in sets satisfying some constraint, in order to prevent the identification of the individuals the rows belong to. In this paper we focus on the l-diversity problem, where the possible attributes are distinguished in sensible attributes and quasi-identifier attributes. The goal is to partition the set of rows, where for each set C of the partition it is required that the number of rows having a specific value in the sensible attribute is at most 1/l |C|. We investigate the approximation and parameterized complexity of l-diversity. Concerning the approximation complexity, we prove the following results: (1) the problem is not approximable within factor c ln l, for some constant c 0, even if the input table consists of two columns; (ii) the problem is APX-hard, even if l = 4 and the input table contains exactly 3 columns; (iii) the problem admits an approximation algorithm of factor m (where m + 1 is the number of columns in the input table), when the sensitive attribute ranges over an alphabet of constant size. Concerning the parameterized complexity, we prove the following results: (i) the problem is W[1]-hard even if parameterized by the size of the solution, l, and the size of the alphabet; (ii) the problem admits a fixed-parameter algorithm when both the maximum number of different values in a column and the number of columns are parameters.