ABSTRACT
In Chapter 1, we present an overview of approximation algorithms and metaheuristics as well as an overview for both volumes of this handbook. In this chapter, we discuss in more detail the basic methodologies and apply them to classic problems. These methodologies include the four major ones: restriction (algorithmic and structural), relaxation (numerical and structural), rounding, and transformation. Greedy methods fall in the class of restriction methods (structural), linear programming (LP)-rounding fall under relaxation (numerical) and α https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781351236423/7ef10423-eda9-42b3-a9ea-761fc7500b5b/content/equ_385.tif"/> -vectors, local ratio and primal-dual fall under problem transformation. We also discuss in more detail inapproximability and show that the “original” version of the traveling salesperson problem (TSP) is constant ratio inapproximable.
