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Complexity indices for the traveling salesman problem based on short edge subgraphs

Author

Listed:
  • Dragoš Cvetković

    (Mathematical Institute SANU)

  • Mirjana Čangalović

    (University of Belgrade)

  • Zorica Dražić

    (University of Belgrade)

  • Vera Kovačević-Vujčić

    (University of Belgrade)

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.

Suggested Citation

  • Dragoš Cvetković & Mirjana Čangalović & Zorica Dražić & Vera Kovačević-Vujčić, 2018. "Complexity indices for the traveling salesman problem based on short edge subgraphs," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(3), pages 759-769, September.
    • Handle: RePEc:spr:cejnor:v:26:y:2018:i:3:d:10.1007_s10100-017-0513-8
    DOI: 10.1007/s10100-017-0513-8
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    References listed on IDEAS

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    1. Ulrich Pferschy & Rostislav Staněk, 2017. "Generating subtour elimination constraints for the TSP from pure integer solutions," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(1), pages 231-260, March.
    2. Tomáš Režnar & Jan Martinovič & Kateřina Slaninová & Ekaterina Grakova & Vít Vondrák, 2017. "Probabilistic time-dependent vehicle routing problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(3), pages 545-560, September.
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