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Theory of Computational Complexity, 2nd Edition by Ker-I Ko, Ding-Zhu Du

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Theorem 2.25

Proof

Using the notion of polynomial-time Turing reducibility, it is not hard to show that the search problem of TSP that asks for the minimum-cost tour is equivalent to the above decision problem (see Exercise 2.18). Therefore, the search problem of TSP is also NP-hard. In the following, we show that the approximation to TSP is also NP-hard.

For each graph G with a cost function c on its edges, let denote the cost of ...

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