I am handling a paper as an associate editor that proposed an algorithm that I find to be weak. In fact, I was able to show that a very simple, brute-force approach actually has a better running time than their algorithm. Therefore, I will recommend rejecting this paper. Do I have an obligation to share my proof that the brute-force running time is better? I want the higher-level editors to have confidence in the rejection, but it also occurs to me that I might be able to improve my own result and publish it independently. Is this a violation of ethics?
UPDATE: Well this certainly took off! I would like to add the following:
The overwhelming consensus is that it would be unethical for me to "scoop" the other authors, so I will not do that. The advice from all is greatly appreciated.
The journal is the top in its field, so we have to be extremely selective. The problem proposed is fairly interesting, but overall the paper does not meet our threshold.
When I say that brute force is better than their method, I mean it in a provable, big O sense.
The authors' proposed scheme is not only inefficient, it is written in a very confusing way. In fact, I asked them to compare their approach to brute-force as a way of helping them clarify their argument, and they did a bad job of it, which is what led me to look into it in the first place.
The fact that brute force performs better than their scheme is not totally trivial because it relies on a combinatorial argument that is not amazing, but not completely obvious either.
I will share my proof with the Editor in chief, but I have decided not to give it to the authors; I will consider publishing independently in the future if their work ever appears elsewhere.
Their paper is not on arXiv or any other website.