TSP Escapes the $O(2^n n^2)$ Curse
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914812469968896 |
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| author | Stoian, Mihail |
| author_facet | Stoian, Mihail |
| contents | The dynamic programming solution to the traveling salesman problem due to Bellman, and independently Held and Karp, runs in time $O(2^n n^2)$, with no improvement in the last sixty years. We break this barrier for the first time by designing an algorithm that runs in deterministic time $2^n n^2 / 2^{Ω(\sqrt{\log n})}$. We achieve this by strategically remodeling the dynamic programming recursion as a min-plus matrix product, for which faster-than-naïve algorithms exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03018 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | TSP Escapes the $O(2^n n^2)$ Curse Stoian, Mihail Data Structures and Algorithms Computational Complexity The dynamic programming solution to the traveling salesman problem due to Bellman, and independently Held and Karp, runs in time $O(2^n n^2)$, with no improvement in the last sixty years. We break this barrier for the first time by designing an algorithm that runs in deterministic time $2^n n^2 / 2^{Ω(\sqrt{\log n})}$. We achieve this by strategically remodeling the dynamic programming recursion as a min-plus matrix product, for which faster-than-naïve algorithms exist. |
| title | TSP Escapes the $O(2^n n^2)$ Curse |
| topic | Data Structures and Algorithms Computational Complexity |
| url | https://arxiv.org/abs/2405.03018 |