Fixed-parameter intractability

Abstract

The authors consider the complexity behavior of parametrized problems that they term fixed-parameter tractability: for each fixed parameter value y the problem is solvable in time O(nc), where c is a constant independent of the parameter y. They introduce a structure theory with which to address the apparent intractability of some parameterized problems, and they obtain completeness, density, and separation/collapse results. The greatest appeal of the theory is in the wide range of natural problems to which it can be applied, and in the practical significance of fixed-parameter problem complexities. Technical aspects are also interesting.