Techniques for designing fixed parameter algorithms

Fixed parameter approach is one of the theoretically rich and useful design technique to deal with NP-completeness. It analizes running times both in terms of input size and the parameter. The fixed parameter O(1) tractable problems can be solved in time f (k)*n^O(1)(where n is the size of the given object) for some computable function f. Three design techniques: depth-bounded search trees, kernelization, and iterative compression to develop fixed parameter algorithms are surveyed in this paper. All techniques are described with respect to vertex cover problem.