I love working on problems like these. If the specifics of the "circles" are written down anywhere, or if you care to describe them, I'd happily give it a whack. I won't claim to be an expert, but I enjoy complex problem solving tasks like this one too much not to offer.
My understanding is that there is a lot of writings produced internally by SingInst that are not available to the public. If you think you are up to the task of organizing and polishing them into publishable form (which I guess probably also requires filling in lots of missing pieces) you should contact them and volunteer. (But I guess they probably don't want to hand their unfinished work to just anyone so you'll have to prove yourself somehow.)
If you just want to get an idea of the issues involved, here are some of my writings on the topic:
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Previously: round 1, round 2, round 3
From the original thread:
Ask away!