Should I cite my own research demonstration paper?
You should always cite your own previous work on a subject just the same as if it were written by someone else. Failure to do so is Self Plagiarism, which is a real thing, oddly enough. 

However, you can also, as you suggest go in to more detail on the algorithm if it will help support the new work. 

The general rule is that when something has been published, using it should have a citation. 

The reason for the rule is that the original paper may include context that a reader in the future may want to see but can't find without the citation.