The relationship between the symmetric traveling-salesman problem and the minimum spanning tree problem yields a sharp lower bound on the cost of an optimum tour. An efficient iterative method for approximating this bound closely from below is presented. A branch-and-bound procedure based upon these considerations has easily produced proven optimum solutions to all traveling-salesman problems presented to it, ranging in size up to sixty-four cities. The bounds used are so sharp that the search trees are minuscule compared to those normally encountered in combinatorial problems of this type.
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This research has been partially supported by the National Science Foundation under Grant GP-25081 with the University of California. Reproduction in whole or in part is permitted for any purpose of the United States Government.
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Held, M., Karp, R.M. The traveling-salesman problem and minimum spanning trees: Part II. Mathematical Programming 1, 6–25 (1971). https://doi.org/10.1007/BF01584070
- Mathematical Method
- Iterative Method
- Span Tree
- Search Tree
- Minimum Span Tree