Cheap and Secure Web Hosting Provider : See Now

Length of an Edit Script and the Number of Deletions

, , No Comments
Problem Detail: 

I am reading the 1989 paper called "An O(NP) Sequence Comparison Algorithm" by Wu, Manber, Myers, and Miller. The algorithm sounds like a good fit for a project I'm doing at work. I have found some implementations in my target language that I could reuse, but I want to make sure that I understand the algorithm (and the code) because it is so crucial to my project.

I am a ways into the paper, and seem to be understanding it, but there's something important in the abstract that still doesn't make sense to me. This is the relevant portion:

Let $A$ and $B$ be two sequences of length $M$ and $N$ respectively, where without loss of generality $N \ge M$, and let $D$ be the length of a shortest edit script between them. A parameter related to $D$ is the number of deletions in such a script, $P = D/2 - (N - M)/2$. We present an algorithm...

This relationship between $P$, $D$, $N$, and $M$ is not proven in the paper. And when a try using it with a simple example (turning "xy" into "x", for instance), I get a nonsensical answer. Can someone please explain the relationship?

Asked By : sam.bishop
Answered By : D.W.

This is a straightforward consequence of the fact that the edit script only contains insert and delete operations. It follows from a little bit of basic arithmetic -- it's nothing especially deep.

Consider a script that contains $I$ insert operations and $P$ delete operations. Then the total number of operations in the edit script is $I+P$. If we're given that the total number of operations is $D$, we know $D=I+P$. Also we know $M+I-P=N$ (since each insert operation increases the length of the document, and each delete decreases it). Solving these two simultaneous equations yields the relationship you list.

Best Answer from StackOverflow

Question Source : http://cs.stackexchange.com/questions/56607

3200 people like this

 Download Related Notes/Documents

0 comments:

Post a Comment

Let us know your responses and feedback