Take, for example, IBM's patents on alias analysis. You can't patent the abstract concept of alias analysis, even if you describe how to do it in very generic terms on a computer. However, you can probably patent Steensgard's specific, near-linear-time algorithm for doing so: http://www.cs.utexas.edu/users/pingali/CS380C/2007fa/papers/....
Why wouldn't Steensgaard's algorithm be an abstract idea?
There is a difference, since unlike hedging (Bilski) and clearing house (Alice Corp) it is a novel abstract idea. But it is still an abstract idea, and logically, should not be patentable.
Stålmarck's algorithm is a similar case. Can't argue it is not novel, but 100% abstract. Parabix is another.
I tend to think of these things as an engineer, rather than a mathematician. A mathematician will say that all algorithms are abstract ideas. I tend to think that "alias analysis" is the abstract idea, while Steensgaard's algorithm is a specific, concrete way of implementing the idea with desirable properties and trade-offs.
Then, are mergesort and quicksort both patentable as specific, concrete ways of implementing the idea of sorting with desirable properties and trade-offs?
