Abstract
We present the extension of our previous work on complexity indices for the traveling salesman problem (TSP). Since we study the symmetric traveling salesman problem, the instances are represented by complete graphs G with distances between cities as the edge weights. A complexity index is an invariant of an instance I by which the execution time of an exact TSP algorithm for I can be predicted. We consider some subgraphs of G consisting of short edges and define several new invariants related to their connected components. For computational experiments we have used the well-known TSP Solver Concorde. Experiments with instances on 50 vertices with the uniform distribution of integer edge weights in the interval [1, 100] show that there exists a notable correlation between the sequences of selected invariants and the sequence of execution times of the TSP Solver Concorde. We provide logical explanations of these phenomena.
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Acknowledgements
The authors are grateful to two referees whose remarks contributed to the quality of the paper. Support has been obtained from the scientific Projets ON174033, ON174010 and F-159 of the Ministry for Education, Science and Technological Development of the Republic of Serbia.
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Cvetković, D., Čangalović, M., Dražić, Z. et al. Complexity indices for the traveling salesman problem based on short edge subgraphs. Cent Eur J Oper Res 26, 759–769 (2018). https://doi.org/10.1007/s10100-017-0513-8
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DOI: https://doi.org/10.1007/s10100-017-0513-8