An Analysis of Several Heuristics for the Traveling Salesman Problem

@article{Rosenkrantz1977AnAO,
  title={An Analysis of Several Heuristics for the Traveling Salesman Problem},
  author={Daniel J. Rosenkrantz and Richard Edwin Stearns and Philip M. Lewis},
  journal={SIAM J. Comput.},
  year={1977},
  volume={6},
  pages={563-581}
}
Several polynomial time algorithms finding “good,” but not necessarily optimal, tours for the traveling salesman problem are considered. We measure the closeness of a tour by the ratio of the obtained tour length to the minimal tour length. For the nearest neighbor method, we show the ratio is bounded above by a logarithmic function of the number of nodes. We also provide a logarithmic lower bound on the worst case. A class of approximation methods we call insertion methods are studied, and… 

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