On fixed-parameter tractability and approximability of NP optimization problems

Fixed-parameter tractability or NP optimization problems is studied by relating it to approximability of the problems. It is shown that an NP optimization problem is fixed-parameter tractable if it admits a fully polynomial-time approximation scheme, or if it belongs to the class MAX SNP or to the class MIN F+/7(1). This provides strong evidence that no W[1]-hard NP optimization problems belong to these optimization classes and includes a very large class of approximable optimization problems into the class of fixed-parameter tractable problems. Evidence is also demonstrated to support the current working hypothesis in the theory of fixed-parameter tractability. (C) 1997 Academic Press.