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arXiv · 1609.09796

The multi-stripe travelling salesman problem

Eranda Cela·Vladimir Deineko·Gerhard J. Woeginger
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Abstract

In the classical Travelling Salesman Problem (TSP), the objective function sums the costs for travelling from one city to the next city along the tour. In the q-stripe TSP with q larger than 1, the objective function sums the costs for travelling from one city to each of the next q cities along the tour. The resulting q-stripe TSP generalizes the TSP and forms a special case of the quadratic assignment problem. We analyze the computational complexity of the q-stripe TSP for various classes of specially structured distance matrices. We derive NP-hardness results as well as polyomially solvable cases. One of our main results generalizes a well-known theorem of Kalmanson from the classical TSP to the q-stripe TSP.

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Eranda Cela, Vladimir Deineko, Gerhard J. Woeginger. 2016-09-20. The multi-stripe travelling salesman problem. https://arxiv.org/abs/1609.09796

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