Combinatorial Optimization: A Tour d’Horizon

In Chapter 7 we have introduced several basic combinatorial optimization problems, and we have shown in detail how the ellipsoid method and basis reduction together with polyhedral information about these problems can be used to design polynomial time algorithms. In this chapter we give an overview about combinatorial optimization problems that are solvable in polynomial time. We also survey important theorems that provide polyhedral descriptions of the polytopes associated with these problems. We indicate how these results can be employed to derive polynomial time algorithms based on the ellipsoid method and basis reduction. The results of this chapter are presented in a condensed form, to cover as much material as possible.