Even a P=NP result doesn't tell us that NP problems have efficient solutions. That depends entirely on
- if the solution is constructive,
- if the asymptotic solution has good constants (lower bound on input size, highest degree term), and
- having no other mitigating factors (requiring absurd amounts of space, for example)
The idea that P=efficient is a complete misnomer. For simple algorithms, asymptotic analysis is a fine enough coarse-grained view of program performance. However for extreme cases (like may be the case for P=NP) asymptotic analysis tells you almost nothing at all.
- if the solution is constructive,
- if the asymptotic solution has good constants (lower bound on input size, highest degree term), and
- having no other mitigating factors (requiring absurd amounts of space, for example)
The idea that P=efficient is a complete misnomer. For simple algorithms, asymptotic analysis is a fine enough coarse-grained view of program performance. However for extreme cases (like may be the case for P=NP) asymptotic analysis tells you almost nothing at all.