A Polynomial-Time Heuristic for the Travelling Salesman Problem Verified Against Held-Karp
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| Natura: | Recurso digital |
| Lingua: | inglese |
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Zenodo
2025
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| _version_ | 1866902163705298944 |
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| author | Aggarwal, Minakshi |
| author_facet | Aggarwal, Minakshi |
| contents | <p><strong>This work presents a polynomial-time structural beam search algorithm for the Traveling Salesman Problem (TSP). The method combines bounded beam expansion with a restricted 2-opt repair step, ensuring polynomial bounds on both time and space. Experimental validation was carried out on symmetric, asymmetric, and blocked matrices for problem sizes up to n = 100. For n ≤ 15, the algorithm’s outputs were verified against the Held–Karp exact method, with complete agreement. Beyond this range, stress tests demonstrated empirical polynomial behavior, with runtime growth around O(n^{3.4}) and memory growth between O(n^{1.2}) and O(n^{1.7}). These results highlight the scalability and reliability of the approach, providing a new structural heuristic framework for combinatorial optimization</strong></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17018248 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Polynomial-Time Heuristic for the Travelling Salesman Problem Verified Against Held-Karp Aggarwal, Minakshi Travelling Salesperson Problem(TSP), Polynomial-Time Algorithms, Structural Beam Search, Combinatorial Optimization, Heuristics, Complexity Analysis <p><strong>This work presents a polynomial-time structural beam search algorithm for the Traveling Salesman Problem (TSP). The method combines bounded beam expansion with a restricted 2-opt repair step, ensuring polynomial bounds on both time and space. Experimental validation was carried out on symmetric, asymmetric, and blocked matrices for problem sizes up to n = 100. For n ≤ 15, the algorithm’s outputs were verified against the Held–Karp exact method, with complete agreement. Beyond this range, stress tests demonstrated empirical polynomial behavior, with runtime growth around O(n^{3.4}) and memory growth between O(n^{1.2}) and O(n^{1.7}). These results highlight the scalability and reliability of the approach, providing a new structural heuristic framework for combinatorial optimization</strong></p> |
| title | A Polynomial-Time Heuristic for the Travelling Salesman Problem Verified Against Held-Karp |
| topic | Travelling Salesperson Problem(TSP), Polynomial-Time Algorithms, Structural Beam Search, Combinatorial Optimization, Heuristics, Complexity Analysis |
| url | https://doi.org/10.5281/zenodo.17018248 |