>> It's simply that construction of practical approximation algorithms or heuristics that work on large instance is (in general) much easier than separating pro

>> It's simply that construction of practical approximation algorithms or heuristics that work on large instance is (in general) much easier than separating proofs for complexity classes. I agree, but the search for better algorithms is also more principled. At some point, separating complexity classes looks like counting the number of angels on a pinhead. It's probably interesting in an abstract way for some people - but it's not my cup of tea, as they say.