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Parameterized complexity of k-anonymity: hardness and tractability

Author

Listed:
  • Paola Bonizzoni

    (Univ. Milano-Bicocca)

  • Gianluca Della Vedova

    (Univ. Milano-Bicocca)

  • Riccardo Dondi

    (Università degli Studi di Bergamo)

  • Yuri Pirola

    (Univ. Milano-Bicocca)

Abstract

The problem of publishing personal data without giving up privacy is becoming increasingly important. A precise formalization that has been recently proposed is the k-anonymity, where the rows of a table are partitioned into clusters of sizes at least k and all rows in a cluster become the same tuple after the suppression of some entries. The natural optimization problem, where the goal is to minimize the number of suppressed entries, is hard even when the stored values are over a binary alphabet or the table consists of a bounded number of columns. In this paper we study how the complexity of the problem is influenced by different parameters. First we show that the problem is W[1]-hard when parameterized by the value of the solution (and k). Then we exhibit a fixed-parameter algorithm when the problem is parameterized by the number of columns and the number of different values in any column. Finally, we prove that k-anonymity is still APX-hard even when restricting to instances with 3 columns and k=3.

Suggested Citation

  • Paola Bonizzoni & Gianluca Della Vedova & Riccardo Dondi & Yuri Pirola, 2013. "Parameterized complexity of k-anonymity: hardness and tractability," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 19-43, July.
    • Handle: RePEc:spr:jcomop:v:26:y:2013:i:1:d:10.1007_s10878-011-9428-9
    DOI: 10.1007/s10878-011-9428-9
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    References listed on IDEAS

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    1. Paola Bonizzoni & Gianluca Della Vedova & Riccardo Dondi, 2011. "Anonymizing binary and small tables is hard to approximate," Journal of Combinatorial Optimization, Springer, vol. 22(1), pages 97-119, July.
    2. Patricia A. Evans & H. Todd Wareham & Rhonda Chaytor, 2009. "Fixed-parameter tractability of anonymizing data by suppressing entries," Journal of Combinatorial Optimization, Springer, vol. 18(4), pages 362-375, November.
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