In this chapter, we will present constant factor algorithms for two fundamental problems, metric Steiner tree and metric TSP. The reasons for considering the metric case of these problems are quite different. For Steiner tree, this is the core of the problem — the rest of the problem reduces to this case. For TSP, without this restriction, the problem admits no approximation factor, assuming P ≠ NP. The algorithms, and their analyses, are similar in spirit, which is the reason for presenting these problems together.
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