Question: 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.

Answer: 
Does running time actually matter? 

It's a program for a paper, not something to be distributed and run commercially on many machines. Perhaps they coded it the way they did because that algorithm is more readable and understandable than a brute force approach. 

For example, if something in my paper required me to do something simple like add up the numbers from 1 to n, we all know the sum is equal to n(n+1)/2, but having a loop that goes from 1 to n and adds them together is simpler to read. 

Assuming this is the only 'lousy' thing in the paper that you take issue with, I don't see it as a reason to reject. If you could come up with a brute force approach that quickly, surely they could as well. Perhaps ask them why they chose that algorithm, or ask a senior editor at your paper for a second opinion, not random strangers on the internet.

As far as using the algorithm you wrote yourself goes, the other answers have adequately stated that that would be incredibly unethical.
As addition to [xLeitix very thoughtful answer](https://academia.stackexchange.com/a/99491/54543) I would give the authors a period of grace (say half a year or so, depending on the typical time scales of your discipline).

If by then they did not publish an improved version matching the performance of your ideas from now, I would regard the confidentiality period to be over and the subject to be fair game for everyone including you.

If they published the poor version somewhere else you should cite them. Do not copy from their submitted previous manuscript. Conduct your own research and present it as such.

If you tell them now about a possible way to improve it's because you want them to improve and publish a better version. If they don't, you could still do it on your own then. But you would have to wait to find out.

The waiting period is the key here and without it you are indeed acting unethically. The waiting period must be really quite generous. However, it should not be infinitely long because otherwise as an editor (or reviewer) you would unfairly restrict yourself in possible research if all topics you ever got to see were inaccessible to you in the future.