Fixed-Parameter Tractability

Abstract

In this chapter, we introduce parameterized problems and the notion of fixed-parameter tractability. We start with an informal discussion that highlights the main issues behind the definition of fixed-parameter tractability. In Sect. 1.2, we begin the formal treatment. In Sect. 1.3, we consider a larger example that introduces some of the most fundamental parameterized problems and the most basic technique for establishing fixed-parameter tractability, the method of bounded search trees. In Sect. 1.4 and Sect. 1.5 we exemplify how the parameterized approach may help to gain a better understanding of the complexity of fundamental algorithmic problems by considering applications in two different areas, approximation algorithms and automated verification. Finally, in Sect. 1.6, we give several equivalent characterizations of fixed-parameter tractability.