> ... a non-combinatorial approach
> to hard optimization problems that
> ... finds better approximations than
> the current state-of-the-art.
So it appears that they're finding approximate solutions, so already it's rather less significant than the title suggests.
Then:
> We show empirical evidence that
> our solver scales linearly with
> the size of the problem, ...
We know that for most NP-Complete problems, most instances are easy. The question then is whether they are testing their algorithms on instances that are known to be hard. There's a chance they're doing something like finding factors of random integers, which we know is easy in almost every instance.
Then:
We know that for most NP-Complete problems, most instances are easy. The question then is whether they are testing their algorithms on instances that are known to be hard. There's a chance they're doing something like finding factors of random integers, which we know is easy in almost every instance.I'm deeply pessimistic.