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. © 2011 Springer-Verlag GmbH.
CITATION STYLE
Dondi, R., Mauri, G., & Zoppis, I. (2011). On the complexity of the l-diversity problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6907 LNCS, pp. 266–277). https://doi.org/10.1007/978-3-642-22993-0_26
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