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Published online by Cambridge University Press: 14 November 2024
In this chapter and Chapter 8, we describe a constant-factor approximation algorithm for the Asymmetric TSP. Such an algorithm was first devised by Svensson, Tarnawski, and Végh. We present the improved version by Traub and Vygen, with an additional improvement that has not been published before.
The overall algorithm consists of four main components, three of which we will present in this chapter. First, we show that we can restrict attention to instances whose cost function is given by a solution to the dual LP with laminar support and an additional strong connectivity property. Second, we reduce such instances to so-called vertebrate pairs. Third, we will adapt Svensson’s algorithm from Chapter 6 to deal with vertebrate pairs. The remaining piece, an algorithm for subtour cover, will be presented in Chapter 8.
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