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Published online by Cambridge University Press: 14 November 2024
Like in the asymmetric case (cf. Chapter 9), one can consider the generalization of Symmetric TSP where the start and end of the tour that we are looking for are not necessarily identical. Christofides’ algorithm can be generalized to this problem but only yields a 5/3-approximation here.
This chapter contains basic results about this problem and also a further generalization called T-tours; these results will be used in subsequent chapters where we will present better approximation algorithms. One important observation is that the "narrow cuts" of an LP solution have a nice structure.
For unweighted graphs, a 3/2-approximation algorithm can be obtained with the techniques of Chapter 13, or with a simple LP-based approach that we will present in this chapter.
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