Fixed-Parameter Tractability and Completeness II: On Completeness for W[1]

Abstract For many fixed-parameter problems that are trivially solvable in polynomial-time, such as k -DOMINATING SET, essentially no better algorithm is presently known than the one which tries all possible solutions. Other problems, such as FEEDBACK VERTEX SET, exhibit fixed-parameter tractability : for each fixed k the problem is solvable in time bounded by a polynomial of degree c , where c is a constant independent of k . In a previous paper, the W Hierarchy of parameterized problems was defined, and complete problems were identified for the classes W [ t ] for t ⩾ 2. Our main result shows that INDEPENDENT SET is complete for W [1].

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