I got puzzled by the definition of ‘substantial similarity’.

Here is the case. I dealt with two related problems, say **P1** and **P2**, that could be treated in the same mathematical framework. I aimed to show optimal appoaches to both problems. Perhaps more details:

**P1**: the optimality criterion was already there (which alone was an open problem for quite a long time, like tens of years) and the tool was also ready. So I’d like to say, if one realized the criterion and the tool, the problem could be solved easily following some standard techniques. But no one recognized this before. In the paper, we examined three different approaches, with different preprocessing before applying the basic idea.

**P2**: the optimality criterion was not recognized. We proved it, which turned out to be of the same sense of **P1** but still different. The tool for solving this problem was also not ready, and we proved it almost from scratch (like 5 pages long), which we thought as the most significant contribution. Some discussions and applications were also involved in the paper.

We did not find a unifying theme to put the two into a page-limited conference submission, while stating related aspects in a clear manner. We also believed each had enough contributions. So we submitted two papers to the same conference. Following the conference guidelines, we tried to rephrase some common preliminary in the two papers, and cited **P1** in **P2** for some common issues and also for clearly stating the contribution of **P2** over **P1**.

However, the two papers were deemed to be ‘substantially similar’ to each other. I searched for what it really means and what is a criterion, but failed. So can anyone share any experience on this? Maybe I just should not submit two related works to the same conference?

Thanks.