I was trying to solve a sub-problem as part of a greater problem for which I am writing a paper to propose a solution.
I'd been working on it for quite a while, when I had the thought that it could be transformed into a special case of one of the most famous and well researched problems in computer science.
I spent about a month doing that transformation while working on other things. All the while though, I was thinking: "Someone else must have had this idea -- its too good not to have had." I didn't spend too much time searching for it, though, because I needed an implementation and not just an idea. I finished up the method about a week ago, and ran it, and found it to work excellently.
Today, I finally found a paper where someone did have the idea. Almost identical to mine (I'm really not at all displeased by this) There are, as expected, a few differences, but nothing I can't explain in a few sentences.
So the question is, in my writeup I could say:
- 1a. We extend the method of X, by adding ...
- 1b. Our method is based on the method of X, but with the following variations...
- 2a. The method we propose is very similar to the method of X, except ...
- 2b. This method is similar to that of X, but developed independently. It has the following difference.
The options 2a/b are what actually occurred. However, I wonder if I should not write instead 1a, or 1b because they provide a better narrative. I've been told paper narrative is important.
I don't like the way 2b sounds, even if it is the most truthful. It sounds like I feel I have something to prove.
Is it generally worth distorting the actual order of events, for a clean narrative?