Management Science and Financial Engineering

The Korean Operations Research and Management Science Society (한국경영과학회)
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Note on the Inverse Metric Traveling Salesman Problem Against the Minimum Spanning Tree Algorithm

  • Received : 2014.03.14
  • Accepted : 2014.05.12
  • Published : 2014.05.30
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Abstract

In this paper, we consider an interesting variant of the inverse minimum traveling salesman problem. Given an instance (G, w) of the minimum traveling salesman problem defined on a metric space, we fix a specified Hamiltonian cycle $HC_0$. The task is then to adjust the edge cost vector w to w' so that the new cost vector w' satisfies the triangle inequality condition and $HC_0$ can be returned by the minimum spanning tree algorithm in the TSP-instance defined with w'. The objective is to minimize the total deviation between the original and the new cost vectors with respect to the $L_1$-norm. We call this problem the inverse metric traveling salesman problem against the minimum spanning tree algorithm and show that it is closely related to the inverse metric spanning tree problem.

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References

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