2026-07-26T00:47:50Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:13970 2024-03-06T10:53:01Z ddc:004 open_access

String Sanitization Under Edit Distance: Improved and Generalized Mieno, Takuya Pissis, Solon P. Stougie, Leen Sweering, Michelle string algorithms data sanitization edit distance dynamic programming 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 (Edit distance, Total order, Frequency, Sanitization) 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 (and thus the frequency) 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 patterns, the ETFS problem asks for transforming W to preserve its privacy and its utility [Bernardini et al., ECML PKDD 2019]. ETFS can be solved in 𝒪(n²k) time [Bernardini et al., CPM 2020]. The same paper shows that ETFS cannot be solved in 𝒪(n^{2-δ}) time, for any δ > 0, unless the Strong Exponential Time Hypothesis (SETH) is false. Our main results can be summarized as follows: - An 𝒪(n²log²k)-time algorithm to solve ETFS. - An 𝒪(n²log²n)-time algorithm to solve AETFS (Arbitrary lengths, Edit distance, Total order, Frequency, Sanitization), a generalization of ETFS in which the elements of 𝒮 can have arbitrary lengths. Our algorithms are thus optimal up to subpolynomial factors, unless SETH fails. In order to arrive at these results, we develop new techniques for computing a variant of the standard dynamic programming (DP) table for edit distance. In particular, we simulate the DP table computation using a directed acyclic graph in which every node is assigned to a smaller DP table. We then focus on redundancy in these DP tables and exploit a tabulation technique according to dyadic intervals to obtain an optimal alignment in 𝒪̃(n²) total time. Beyond string sanitization, our techniques may inspire solutions to other problems related to regular expressions or context-free grammars. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Takuya Mieno and Solon P. Pissis and Leen Stougie and Michelle Sweering 2021 Is Part Of LIPIcs, Volume 191, 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CPM.2021.19 urn:nbn:de:0030-drops-139709 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2021.19 eng https://creativecommons.org/licenses/by/4.0/legalcode