Approximation of max independent set, min vertex cover and related problems by moderately exponential algorithms

Using ideas and results from polynomial approximation and exact computation we design approximation algorithms for several NP-hard combinatorial problems achieving ratios that cannot be achieved in polynomial time (unless a very unlikely complexity conjecture is confirmed) with worst-case complexity much lower (though super-polynomial) than that of an exact computation. We study in particular max independent set, min vertex cover and then we extend results to max clique, max bipartite subgraph and max set packing.