Most problems in this space have reasonable-time approximations that get you close to the right answer for far less computational complexity. Even without ever having looked at Steiner trees before, I guess that there were reasonable approximations, and confirmed that was true without looking too hard. Letting Patterson know about the problem mapping ("your problem is an instance of <X>") is typically enough for a person of his calibre to research approximate solutions good enough for him to run some experiments.
(many people say the protein folding problem is NP-complete, but the community generally believes you can predict the folding pathways of all proteins without explicitly running such calculations).
> typically enough for a person of his calibre to research approximate solutions good enough for him to run some experiments
And it's hard to overstate his caliber. For those of you who are unfamiliar with the name, Nick mentored Clifford Cocks at GCHQ and pushed him in the direction of inventing public key cryptography.
(many people say the protein folding problem is NP-complete, but the community generally believes you can predict the folding pathways of all proteins without explicitly running such calculations).