I believe that if we define Damerau-Levenshtein distance as “minimum number of operations needed to transform one string into the other, where an operation is defined as an insertion, deletion, or substitution of a single character, or a transposition of two characters” (as it is done in Wikipedia, and also in this http://portal.acm.org/citation.cfm?id=356827.356830 article, where the notion seems to be introduced for the first time), then an algorithm calculating this distance should return 2 for (“TO”, “OST”). Otherwise the algorithm is calculating something else

But that doesn’t actually matter. Sorry for the long comment, and thank you for your answer!

“the number of edit operations needed to make the strings equal under the condition that no substring is edited more than once“

You and I both know the edit distance between ‘TO’ and ‘OST’ is 2 (swap T for O to get OT, insert S), but Damerau Levenshtein works on single operations on the original string. The ‘OT’ is an intermediate result (a substring that has been previously edited). The wikipedia article does mention improved algorithms for what is described as “a proper algorithm to calculate unrestricted Damerau–Levenshtein distance”. I suspect if it gives you a different result to the original algorithm, it possibly isn’t ‘Damerau-Levenshtein’! Maybe one day I’ll get round to having a look at those other algorithms, but there’s absolutely no chance in the next few months.

(You can see the result in question on the damerau-levenshtein page at spider.my)

Thanks for your implementations!
I noticed that damlev(“TO”,”OST”) returns 3, while it should be 2 in this case (the test actually is from Wikipedia article on Damlev distance).
Do you think it can be fixed?

Thanks!

If you can send me an example of a bad return value, I’ll check it out as soon as I can.

–update 2009 Aug 15 New version with regression fixed (and added to static main method tests) uploaded same day. Forgot to update my comment here!

Thanks for providing your Leveshtein methods.

I believe I found a bug with the damlevlim method. I think it’s easiest described by the following example:

damlevlim(“short”,”shoort”,2);
Result: 2 (should be 1)

damlevlim(“short”,”shrt”,2);
Result: 2 (should be 1)

As you can see the second string has an additional character or is missing a character inside the string.

Can you take a look at it?

Best regards
/Björn Törnqvist