Geometric Concepts

Abstract

Many traveling salesman problem instances arising in practice have the property that they are defined by point sets in the 2-dimensional plane (e.g., drilling and plotting problems to be discussed in Chapter 11). Though true distances can usually be not given exactly or only by very complicated formulae, they can very well be approximated by metric distances. To speed up computations we can therefore make use of geometric properties of the point set. In this chapter we introduce concepts for deriving informations about the structure of point sets in the plane and review some basic algorithms. A textbook on computational geometry is Edelsbrunner (1987).