When learning about computational complexity I find that when discussing the NP-Complete problems authors always give examples of such problems that can in fact be solved in poly time.

I understand this as a teaching aide but to fail to follow up a quick runtime example with the same example now with the added necessary complexity to cause it to be NP-hard seems an unfortunate omission.

What I was wondering was if someone could show me an example of an 0-1 integer programming problem that if solved in polynomial time would grab a unicorn by the horn.

for example.. and i know integer factorization has yet to find its place in the complexity spectrum but talking about the difficulty of integer factorization and then explaining the process as finding that 21=3x7 does little to show someone trying to understand the algorithms for the problem, whereas showing an individual the RSA challenge problems makes clear the difficulties in the problem and grants an 'if an algo solves one of these in poly then the complexity of factorization is definitely in P'

When learning about computational complexity I find that when discussing the NP-Complete problems authors always give examples of such problems that can in fact be solved in poly time.

I understand this as a teaching aide but to fail to follow up a quick runtime example with the same example now with the added necessary complexity to cause it to be NP-hard seems an unfortunate omission.

What I was wondering was if someone could show me an example of an 0-1 integer programming problem that if solved in polynomial time would grab a unicorn by the horn after having its logic's generality proved.

for example.. and i know integer factorization has yet to find its place in the complexity spectrum but talking about the difficulty of integer factorization and then explaining the process as finding that 21=3x7 does little to show someone trying to understand the algorithms for the problem, whereas showing an individual the RSA challenge problems makes clear the difficulties in the problem and grants an 'if an algo solves all of these and subsequently any factoring effort in poly then the complexity of factorization is definitely in P'

When learning about computational complexity I find that when discussing the NP-Complete problems authors always give examples of such problems that can in fact be proven in poly time.

I understand this as a teaching aide but to fail to follow up a quick runtime example with the same example now with the added necessary complexity to cause it to be NP-hard seems an unfortunate omission.

What I was wondering was if someone could show me an example of an 0-1 integer programming problem that if solved in polynomial time would grab a unicorn by the horn.

for example.. and i know integer factorization has yet to find its place in the complexity spectrum but talking about the difficulty of integer factorization and then explaining the process as finding that 21=3x7 does little to show someone trying to understand the algorithms for the problem, whereas showing an individual the RSA challenge problems makes clear the difficulties in the problem and grants an 'if an algo solves one of these in poly then the complexity of factorization is definitely in P'

When learning about computational complexity I find that when discussing the NP-Complete problems authors always give examples of such problems that can in fact be solved in poly time.

I understand this as a teaching aide but to fail to follow up a quick runtime example with the same example now with the added necessary complexity to cause it to be NP-hard seems an unfortunate omission.

What I was wondering was if someone could show me an example of an 0-1 integer programming problem that if solved in polynomial time would grab a unicorn by the horn.

for example.. and i know integer factorization has yet to find its place in the complexity spectrum but talking about the difficulty of integer factorization and then explaining the process as finding that 21=3x7 does little to show someone trying to understand the algorithms for the problem, whereas showing an individual the RSA challenge problems makes clear the difficulties in the problem and grants an 'if an algo solves one of these in poly then the complexity of factorization is definitely in P'