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from Part II - Concepts and Techniques
Published online by Cambridge University Press: 18 April 2019
In this chapter, we introduce the concepts of parameterized problem and fixed-parameter tractability. Using these concepts, one can show that problems that are polynomial-time intractable in general (i.e., \np-hard) may yet be practically solvable provided only that certain input parameters are constrained in terms of their values. This conception of tractability underlies the FPT-Cognition Thesis introduced in Chapter 1. We illustrate three techniques for showing that a parameterized problem is fixed-parameter tractable, namely, brute-force combinatorics, bounded search trees, and reduction to a problem kernel.We also include several exercises for practicing these techniques.
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