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Fixed-parameter tractability and completeness II: On completeness for W[1]. (English) Zbl 0873.68059
Summary: 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 $$t\geq 2$$. Our main result shows that INDEPENDENT SET is complete for W[1].

##### MSC:
 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
independent set
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##### References:
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