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تسجيل مستخدم جديدA Simple Sublinear Algorithm for Gap Edit Distance
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We study the problem of estimating the edit distance between two $n$-character strings. While exact computation in the worst case is believed to require near-quadratic time, previous work showed that in certain regimes it is possible to solve the following {em gap edit distance} problem in sub-linear time: distinguish between inputs of distance $le k$ and $>k^2$. Our main result is a very simple algorithm for this benchmark that runs in time $tilde O(n/sqrt{k})$, and in particular settles the open problem of obtaining a truly sublinear time for the entire range of relevant $k$. Building on the same framework, we also obtain a $k$-vs-$k^2$ algorithm for the one-sided preprocessing model with $tilde O(n)$ preprocessing time and $tilde O(n/k)$ query time (improving over a recent $tilde O(n/k+k^2)$-query time algorithm for the same problem [GRS20].
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