The multi-stripe travelling salesman problem
Discrete Mathematics
2016-10-03 v1 Combinatorics
Optimization and Control
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.
Keywords
Cite
@article{arxiv.1609.09796,
title = {The multi-stripe travelling salesman problem},
author = {Eranda Cela and Vladimir Deineko and Gerhard J. Woeginger},
journal= {arXiv preprint arXiv:1609.09796},
year = {2016}
}