Polynomial Time Convergence for NP-Complete Problems via Bounded Carry Algebra: A Hierarchical Reduction Algorithm for the Subset Sum Problem
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2026
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| _version_ | 1866901492109148160 |
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| author | 福永, 大河 |
| author_facet | 福永, 大河 |
| contents | <p>This paper presents a deterministic, polynomial-time algorithm (Hierarchical Carry Reduction: HCR) for the Subset Sum Problem, a classic NP-complete problem. By mapping integer sets into a vector space and analyzing carry transitions across hierarchical layers, we demonstrate that the number of active states is strictly bounded by O(n).</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18374114 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Polynomial Time Convergence for NP-Complete Problems via Bounded Carry Algebra: A Hierarchical Reduction Algorithm for the Subset Sum Problem 福永, 大河 <p>This paper presents a deterministic, polynomial-time algorithm (Hierarchical Carry Reduction: HCR) for the Subset Sum Problem, a classic NP-complete problem. By mapping integer sets into a vector space and analyzing carry transitions across hierarchical layers, we demonstrate that the number of active states is strictly bounded by O(n).</p> |
| title | Polynomial Time Convergence for NP-Complete Problems via Bounded Carry Algebra: A Hierarchical Reduction Algorithm for the Subset Sum Problem |
| url | https://doi.org/10.5281/zenodo.18374114 |