Algorithms that run in polynomial time if P=NP

Question

On Wikipedia, it says that that there are some algorithms that would run in polynomial time if and only if P=NP. They gave one example (without citation), but are there any others? I tried looking them up and couldn't find any.

Answer 1

Wikipedia is describing Levin's universal algorithm. This is an algorithm for verifiable problems, which is competitive with the optimal algorithm (in some sense). In particular, the exact same approach would work for any problem in NP, not just SUBSET-SUM.