String Sanitization under Edit Distance

Let W be a string of length n over an alphabet, 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 XED such that: (i) no string of S occurs in XED; (ii) the order of all other length-k substrings overis the same in W and in XED; and (iii) XED 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 . 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(n2-) time, for any> 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. 2012 ACM Subject Classification Theory of computation ! Pattern matching.