Counting Locally Optimal Tours in the TSP
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912084405518336 |
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| author | Manthey, Bodo van Rhijn, Jesse |
| author_facet | Manthey, Bodo van Rhijn, Jesse |
| contents | We show that the problem of counting the number of 2-optimal tours in instances of the Travelling Salesperson Problem (TSP) on complete graphs is #P-complete. In addition, we show that the expected number of 2-optimal tours in random instances of the TSP on complete graphs is $O(1.2098^n \sqrt{n!})$. Based on numerical experiments, we conjecture that the true bound is at most $O(\sqrt{n!})$, which is approximately the square root of the total number of tours. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18650 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting Locally Optimal Tours in the TSP Manthey, Bodo van Rhijn, Jesse Data Structures and Algorithms Computational Complexity Discrete Mathematics We show that the problem of counting the number of 2-optimal tours in instances of the Travelling Salesperson Problem (TSP) on complete graphs is #P-complete. In addition, we show that the expected number of 2-optimal tours in random instances of the TSP on complete graphs is $O(1.2098^n \sqrt{n!})$. Based on numerical experiments, we conjecture that the true bound is at most $O(\sqrt{n!})$, which is approximately the square root of the total number of tours. |
| title | Counting Locally Optimal Tours in the TSP |
| topic | Data Structures and Algorithms Computational Complexity Discrete Mathematics |
| url | https://arxiv.org/abs/2410.18650 |