Back in grad school when I was working on papers, it seemed pretty essential to have an experience PhD involved in the process. No matter how "great" the idea I had, there were always a lot of complications. For example, making sure I had the appropriate literature review done, did controlled comparisons against best of breed algorithms etc. I would write an abstract of your improvements with hard numbers and the conclusions that you draw from them and also a 2 page summary explaining all this, and email it to a friendly applied mathematician.