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String Sanitization Under Edit Distance

Authors Giulia Bernardini , Huiping Chen, Grigorios Loukides , Nadia Pisanti , Solon P. Pissis , Leen Stougie, Michelle Sweering

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Author Details

Giulia Bernardini
  • University of Milano - Bicocca, Milan, Italy
Huiping Chen
  • King’s College London, UK
Grigorios Loukides
  • King’s College London, UK
Nadia Pisanti
  • University of Pisa, Italy
  • ERABLE Team, Lyon, France
Solon P. Pissis
  • CWI, Amsterdam, The Netherlands
  • Vrije Universiteit, Amsterdam, The Netherlands
  • ERABLE Team, Lyon, France
Leen Stougie
  • CWI, Amsterdam, The Netherlands
  • Vrije Universiteit, Amsterdam, The Netherlands
  • ERABLE Team, Lyon, France
Michelle Sweering
  • CWI, Amsterdam, The Netherlands

Funding

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 872539.
  • Bernardini, Giulia: Partially supported by a research internship at CWI.
  • Chen, Huiping: Supported by a Ph.D scholarship from China Scholarship Council.
  • Stougie, Leen: Supported by the Netherlands Organisation for Scientific Research (NWO) through Gravitation-grant NETWORKS-024.002.003.
  • Sweering, Michelle: Supported by the Netherlands Organisation for Scientific Research (NWO) through Gravitation-grant NETWORKS-024.002.003.

Acknowledgements

The authors would like to thank Takuya Mieno (Kyushu University) for proofreading the manuscript.

Cite AsGet BibTex

Giulia Bernardini, Huiping Chen, Grigorios Loukides, Nadia Pisanti, Solon P. Pissis, Leen Stougie, and Michelle Sweering. String Sanitization Under Edit Distance. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 7:1-7:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.CPM.2020.7

Abstract

Let W be a string of length n over an alphabet Σ, k be a positive integer, and 𝒮 be a set of length-k substrings of W. The ETFS problem asks us to construct a string X_{ED} such that: (i) no string of 𝒮 occurs in X_{ED}; (ii) the order of all other length-k substrings over Σ is the same in W and in X_{ED}; and (iii) X_{ED} has minimal edit distance to W. When W represents an individual’s data and 𝒮 represents a set of confidential substrings, algorithms solving ETFS can be applied for utility-preserving string sanitization [Bernardini et al., ECML PKDD 2019]. Our first result here is an algorithm to solve ETFS in 𝒪(kn²) time, which improves on the state of the art [Bernardini et al., arXiv 2019] by a factor of |Σ|. Our algorithm is based on a non-trivial modification of the classic dynamic programming algorithm for computing the edit distance between two strings. Notably, we also show that ETFS cannot be solved in 𝒪(n^{2-δ}) time, for any δ>0, unless the strong exponential time hypothesis is false. To achieve this, we reduce the edit distance problem, which is known to admit the same conditional lower bound [Bringmann and Künnemann, FOCS 2015], to ETFS.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • String algorithms
  • data sanitization
  • edit distance
  • dynamic programming
  • conditional lower bound

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