On fixed-parameter tractability and approximability of NP-hard optimization problems

Abstract

Fixed-parameter tractability and approximability of NP-hard optimization problems are studied based on a model GC(s(n), Pi /sub k//sup L/). The main results are (1) a class of NP-hard optimization problems, including dominating-set and zero-one integer-programing, are fixed-parameter tractable if and only if GC(s(n), Pi /sub 2//sup L/) contained in P for some s(n) in omega (log n); (2) most approximable NP-hard optimization problems are fixed-parameter tractable. In particular, the class MAX NP is fixed-parameter tractable; (3) a class of optimization problems do not have fully polynomial time approximation scheme unless GC(s(n), Pi /sub k//sup L/) contained in P for some s(n) in omega (log n) and for some k>l; and (4) every fixed-parameter tractable optimization problem can be approximated in polynomial time to a non-trivial ratio.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>