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[Solved]: Complexity of edit distance with block operations

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Problem Detail: 

Consider the following problem. I have a pattern $P$ of length $100$ and a text $T$ of length $n$. I want to find the minimum number of operations to transform $P$ into $T$. The operations are:

  • Insert a single character into $P$
  • Delete a single character from $P$
  • Substitute a single character in $P$ for another one
  • Move an entire substring of $P$ to another location in $P$

What is the time complexity of this problem?

Asked By : Lembik

Answered By : lPlant

What it looks like you are after is the Block Swap edit distance. Here is a paper outlining a polynomial time solution to this problem, An Edit Distance Algorithm with Block Swap . I cant recall the exact time complexity they give in the paper, however it is outlined in there.

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Question Source : http://cs.stackexchange.com/questions/27812

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