What should I do with small research results in theoretical computer science? I am a PhD student who works in theory. I was working on some problem for the last 6-7 weeks. After doing a survey for two weeks it took me about four weeks to solve a research problem.

Along with my research supervisor, I was able to solve the research problem, after having a conversion with my research supervisor I came to know that it is a very small result (not yet to publishable), he suggested to do the same kind of work for some closely-related problem and then we can submit by adding something more.

I am very much satisfied with my adviser's opinion. I am just wondering what else I should do in this situation. Should I write it and upload it on arXiv or to do something else.

Please note that I am not going against my research supervisor; I am just wondering what the other possibilities are. I am asking this question because I  am new, not because I don't trust my research supervisor.
In my opinion, nothing new is not publishable. Small results are not prestige-ly enough publishable, that's it.

So, if you want to publish this result, find a venue small enough for it and submit. Another issue, however, if your advisor tells you to wait, you should rather wait.

It might be, namely, that by combining this result with a minor further development, you might seriously bump up its "prestige", i.e. the possibility it gets accepted at a larger or more important venue. Advisors typically know this stuff better than PhD students.



To give you an example. I played once with PGP public keys and found a way to visualize them as a nice image. After a literature research I found that noone did it like this before. So, it was a new scientific result, but not very publishable, just as your issue. Then I thought a bit more, what properties does my visualization have. I found SHA1 collision data, applied my visualization, and saw that I can tell the two files with same hash apart with my approach. Now, this is quite big. (But little work for me.)

I further looked around where to publish it (Visualization or Security), it successfully landed at the Visual Computer.