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I have discovered a (mathematical) graph that plays a crucial role for solving certain hard optimization problems efficiently.
As I see a certain potential to reduce costs, I would like to protect my invention.

I know that software patents are granted in the US, but would that be the case also for newly invented mathematical graphs that are the crucial part of an algorithm?

Have any patents in that vein already been granted?

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You cannot patent a mathematical algorithm. It would be deemed "abstract". What you might be able to do is patent the use of an algorithm for a specific tangible application. I have a few patents like this. This means if your new mathematical graph can be applied to four different problems, you would probably have to apply for four different patents.

Now, I am not an attorney. Algorithm based patents are tricky things and I would strongly encourage you to consult with a patent lawyer with specific experience in the field.

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