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My greatest contribution to scientific progress came in 2010 when I was having lunch with Nick. He described an admixture problem to me, summarizing: "I've got

My greatest contribution to scientific progress came in 2010 when I was having lunch with Nick. He described an admixture problem to me, summarizing: "I've got observed populations and I want to build a tree where I pick points for unobserved populations such that it minimizes the edge length of the tree. I can't seem to come up with a good algorithm for it." "Nick, that's the Steiner Tree problem! It's NP-complete!" He probably would've wasted a few more days going down that rabbit hole. Edit: Nick has some great Cold War spy games stories that I've only heard him tell in broad strokes.

qclibre22 4y ago
Any hope of solving it using quantum computing?
- jjtheblunt 4y ago
  NP-complete isn't necessarily bad, depending on the size of inputs, right?
  - dekhn 4y ago
    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).
    - bhickey 4y ago
      > 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.
- bhickey 4y ago
  Looks like there's a quantum speedup: https://arxiv.org/abs/1904.03581 https://arxiv.org/abs/1904.03581 IIRC there's no epsilon approximation.
- dave18 4y ago
  No. Theory offers you a quadratic speed-up of the exponential worst-case running time. And this is the theory. In practice, it looks worse. ....and: exponential worst-case running time is almost never observed in any kind of practical NP-hard optimization problem when using state-of-the-art algorithms on digital computers... and talking about the Steiner tree problem: It is basically solved for all practical matters. Same for the famous travelling salesman problem. Look at this solver: https://www.math.uwaterloo.ca/tsp/concorde.html https://www.math.uwaterloo.ca/tsp/concorde.html Or look at these amazing results: https://www.math.uwaterloo.ca/tsp/star/index.html https://www.math.uwaterloo.ca/tsp/star/index.html
dave18 4y ago
Sorry, but this was a somewhat bad advise. You can solve huge Steiner tree problems (up to a million of edges) in practice to optimality. See for example this solver: https://scipjack.zib.de/ https://scipjack.zib.de/ There is a wide-spread misconception of the meaning of NP-complete, unfortunately. Also, it should probably be NP-hard, not NP-complete, the latter is for a decision problem only.

qclibre22 4y ago

Any hope of solving it using quantum computing?

jjtheblunt 4y ago
NP-complete isn't necessarily bad, depending on the size of inputs, right?
- dekhn 4y ago
  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).
  - bhickey 4y ago
    > 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.
bhickey 4y ago
Looks like there's a quantum speedup: https://arxiv.org/abs/1904.03581 https://arxiv.org/abs/1904.03581 IIRC there's no epsilon approximation.
dave18 4y ago
No. Theory offers you a quadratic speed-up of the exponential worst-case running time. And this is the theory. In practice, it looks worse. ....and: exponential worst-case running time is almost never observed in any kind of practical NP-hard optimization problem when using state-of-the-art algorithms on digital computers... and talking about the Steiner tree problem: It is basically solved for all practical matters. Same for the famous travelling salesman problem. Look at this solver: https://www.math.uwaterloo.ca/tsp/concorde.html https://www.math.uwaterloo.ca/tsp/concorde.html Or look at these amazing results: https://www.math.uwaterloo.ca/tsp/star/index.html https://www.math.uwaterloo.ca/tsp/star/index.html

dave18 4y ago

Sorry, but this was a somewhat bad advise. You can solve huge Steiner tree problems (up to a million of edges) in practice to optimality. See for example this solver: https://scipjack.zib.de/ https://scipjack.zib.de/ There is a wide-spread misconception of the meaning of NP-complete, unfortunately. Also, it should probably be NP-hard, not NP-complete, the latter is for a decision problem only.