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Published online by Cambridge University Press: 14 November 2024
A major step towards the first constant-factor approximation algorithm for the Asymmetric TSP was made by Svensson. He devised a constant-factor approximation algorithm for Asymmetric Graph TSP, which is the special case of the Asymmetric TSP with c(e)=1 for all e ∈ E.
In this chapter, we present Svensson’s algorithm for the Asymmetric Graph TSP. We also incorporate some improvements, from Traub and Vygen, who gave a variant of Svensson’s algorithm with improved approximation ratio. Moreover, we present an improved algorithm for finding a graph subtour cover, which is the main subroutine of Svensson’s algorithm. Overall, we will obtain an approximation ratio of 8+ε for Asymmetric Graph TSP, for every ε>0.
Almost all techniques presented in this chapter will be used again in Chapters 7 and 8 for the general Asymmetric TSP.
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