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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 an approximation factor $text{poly}(log n)$. In this paper, we provide an algorithm with running time $tilde{O}(n^{2-2/7})$ that approximates the edit distance within a constant factor.
We show that the edit distance between two strings of length $n$ can be computed within a factor of $f(epsilon)$ in $n^{1+epsilon}$ time as long as the edit distance is at least $n^{1-delta}$ for some $delta(epsilon) > 0$.
Computing efficiently a robust measure of similarity or dissimilarity between graphs is a major challenge in Pattern Recognition. The Graph Edit Distance (GED) is a flexible measure of dissimilarity between graphs which arises in error-tolerant graph
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