I am a little confused about some of the language used here.
> The best version they could come up with — a kind of speed limit — comes from the trivial case where the problem’s variables (such as whether a salesman visits a city or not) can only assume binary values (zero or 1).
Did they just call an NP-Complete problem a trivial case?!
I was under the impression that all ILP can be reduced to 01-ILP equivalents, and vice versa?
> Unfortunately, once the variables take a value beyond just zero and 1, the algorithm’s runtime grows much longer. Researchers have long wondered if they could get closer to the trivial ideal.
So, is the work a solver improving the lower bound for 01-ILP or an algorithm that brings the bounds between 01-ILP and general ILP closer?
> The best version they could come up with — a kind of speed limit — comes from the trivial case where the problem’s variables (such as whether a salesman visits a city or not) can only assume binary values (zero or 1).
Did they just call an NP-Complete problem a trivial case?!
I was under the impression that all ILP can be reduced to 01-ILP equivalents, and vice versa?
> Unfortunately, once the variables take a value beyond just zero and 1, the algorithm’s runtime grows much longer. Researchers have long wondered if they could get closer to the trivial ideal.
So, is the work a solver improving the lower bound for 01-ILP or an algorithm that brings the bounds between 01-ILP and general ILP closer?