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Analysis of the Held-Karp lower bound for the asymmetric TSP. (English) Zbl 0768.90079

Summary: We show that the Held-Karp lower bound for the asymmetric traveling salesman problem (ATSP) dominates the Balas-Christofides lower bound. For the ATSP with triangle inequality, we show that it is also greater than \((1/[\lceil\log n\rceil)Z_{\text{TSP}}\), where \(Z_{\text{TSP}}\) is the cost of the optimal tour. In the course of proving these results, we provide alternate characterizations of the Held-Karp lower bound and prove that on instances which obey the triangle inequality, the lower bound is monotonic with respect to the set of nodes included.

MSC:

90C35 Programming involving graphs or networks
90C05 Linear programming
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References:

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