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I was searching for an algorithm that performs better than normal O(nm) edit distance algorithm, and read that it has O(nd) worst case time complexity but couldn't find any proper explanation for it. Can someone please explain how the algorithm works?

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The best explanation of Ukkonen's algorithm is Ukkonen's suffix tree algorithm in plain English? Hope that helps, its not easy one to understand.

Basically Ukkonen's algo allows you to construct a suffix tree quickly. You would then have to traverse the tree to calculate the edit distance.

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