I'm doing a PhD in computer science. I've been working in my research question for a year and a half now and I still didn't publish any article yet. Lately, I found out an idea that can improve the current solutions. I believe my idea can provide better results than current tools. But, my question is as follows: Is it possible to submit my paper to a scientific journal and hopefully get it accepted without implementing my idea (i.e. without testing my idea)?
1) This is a question best addressed to your adviser or someone else familiar with your work, because questions like these often depend on the details of what you're doing.
2) It depends on the subfield, the nature of the work, and what evidence you can provide that the methodology. You need to provide argumentative evidence that your approach is noteworthy and correct. This can be a mathematical proof of correctness, a diagram and five pages of discussion and commentary, or a statistical analysis comparing the algorithm to other similar ones. Which is most appropriate depends on the nature of your work. However, whatever you choose is going to be an involved endeavor, and you have little hope of getting something published if you insist on not doing a meaningful evaluation of its performance.
Assuming that you are willing to evaluate and validate your algorithm, but just not willing or able to implement it...
If you're doing theoretical work, the answer is likely "yes you can publish it". New algorithms for known problems or improvements to the theoretical run-times of established algorithms are often published with formal proofs of correctness rather than implementations. Pseudo-code would be encouraged but is not even always necessary.
If you're doing non-theoretical work, the answer is likely "no you cannot publish it". Non-theoretical CS work of this type is usually backed by numerical experimentation and quantitative comparison to known benchmarks and frequently-used algorithms. In an ideal world, you'd even leverage statistics to improve your analysis.
Ideas are cheap. Most researchers have more ideas than they have time to develop them. It's the development which has value. Or to put it another way, in order to advance the field you need to convince other people that your idea is interesting, and the fact that you believe it will not be sufficient. Depending on your subfield the way to convince people may be a mathematical analysis, empirical measurement of an implementation, or a combination of the two, but you need something.
The reviewers will generally need some evidence that your idea works. That evidence can come in various forms, and doesn't necessarily have to be experimental (e.g. in certain fields you could formally prove something instead). That said, you generally won't be able to publish ideas without any evidence in good venues (unless the reviewers are asleep on the job) -- why would you want to, in any case?
To put it another way, you say that you "believe" your idea can provide better results than current tools. Aren't you curious whether or not that's actually the case? Either way, the reviewers are likely to be (assuming you have good reviewers).