Combinatorial Optimization: Some Basic Examples

Abstract

In the remaining part of this book we apply the methods developed in the first part to combinatorial optimization. In this chapter we give some illuminating examples to explain the basic techniques of deriving polynomial time algorithms for combinatorial optimization problems. These techniques are based on combining the ellipsoid method and basis reduction with results from the field called “polyhedral combinatorics”, where combinatorial optimization problems are formulated as linear programs. Chapter 8 contains a comprehensive survey of combinatorial problems to which these methods apply. Finally, in the last two chapters we discuss some more advanced examples in greater detail.