P=NP, what do you do?
carterschonwald: If you have an algorithm with a worst case polynomial bound on the time it takes to solve an NP complete problem, then UPS, Fedex and other companies would pay nicely to use a service to optimally do scheduling, routing and resource allocation.On the other hand, since it is more likely that P!=NP, this "almost" algorithm probably fails exponentially on some set of examples, and in practice there are plenty of NP complete problems which enjoy very good approximation algorithms or heuristic algorithms which work well for typical problem instances.