Edit distance is a measure of similarity of two strings based on the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. The edit distance can be computed exactly using a dynamic programming algorithm that runs in quadratic time. Andoni, Krauthgamer and Onak (2010) gave a nearly linear time algorithm that approximates edit distance within approximation factor poly(log n). In this paper, we provide an algorithm with running time O(n 2−2/7 ) that approximates the edit distance within a constant factor. k is the Ulam distance of the input; this was improved by Naumovitz et al. [20] to a (1 + ε)-factor approximation (for any ε > 0) with similar runtime. Our results. We present the first truly sub-quadratic time 979
Recently, Chakraborty et al. gave a truly subquadratic algorithm that approximates the edit distance to within a constant factor REF .
Approximating Edit Distance within Constant Factor in Truly Sub-Quadratic Time
2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
Mathematics Computer Science