I am looking for an algorithm that checks if the Levenshtein distance between two strings $s_1$ and $s_2$ is less than a certain upper bound $B$. I know, there are plenty of algorithms for calculating the Levenshtein distance, but I expect a possible efficiency gain in scenarios where $B$ << $Levenshtein(s_1, s_2)$, because an algorithm not aiming to determine the actual distance, but just aiming to answer the question whether the distance is below $B$ or not, can terminate earlier, as soon as it becomes clear that the distance must surpass $B$.
For such an algorithm, I have the idea of using a recursive function which takes the parameters $s_1$, $s_2$ and $B$ checks if the first character of $s_1$ and $s_2$ are equal, and recursively calls itself (with a potentially decremented $B$ and accordingly adapted $s_1$ and $s_2$). The function would sort out all scenarios where $B$ falls below 0. (And of course, the function will make use of the trivial lower bounds of $Levenshtein(s_1, s_2)$.) If no recursion branch is left, the algorithm would terminate, asserting $Levenshtein(s_1, s_2) \geq B$.
But before reinventing the wheel, I wanted to ask if there are already existing solutions for my problem. I googled this and didn't find any, but maybe my google results were just polluted with the Levenshtein Distance Algorithms. If there is no such algorithm yet, is my approach a good idea, or are there more efficient ways which I oversee?
I googled this and didn't find anytry with Levenshtein|Левенште́йн - you should find, amongst others, Ukkonen. – greybeard Sep 28 '20 at 09:58