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Published online by Cambridge University Press: 14 November 2024
A natural generalization of the (asymmetric) traveling salesman problem arises when we are given a start vertex s and an end vertex t and ask for a tour that begins in s and ends in t, rather than a round trip.
While this problem seems to be harder, we will see in this chapter that it can be tackled by similar techniques. In particular, we show black-box reductions (by Feige and Singh, and by Köhne, Traub, and Vygen) to Asymmetric TSP and prove, as new results, the best-known approximation ratios and bounds on the integrality ratio of the natural LP relaxation.
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