Moderate exponential time approximation and branching algorithms

We study links between approximation, exponential time computation and fixed parameter tractability. In particular, rather than focusing on one particular optimization problem, we tackle the question of finding sufficient conditions for a problem to admit “good” approximation algorithms in exponential time. In particular, we focus on the existence of “approximation schemata” (ratios 1 ± ǫ for arbitrarily small ǫ) and we exhibit conditions under which a technique of devising approximate branching algorithms reaches interesting results.