Optimization Problems, Approximation Schemes, and Their Relation with FPT
Optimization problems are at the heart of complexity theory. In practice, we usually wish to optimize some objective function (e.g., find a least-cost tour) rather than solve a related decision problem. Furthermore, even if we demonstrate that some problem has no fast solution, it is often acceptable to find an approximate solution to some desired performance ratio. In this section, we will see that parametric complexity and approximatibility are deeply related.
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