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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2504.18640 |
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| _version_ | 1866908338080448512 |
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| author | Fu, Cheng-Hao Lincoln, Andrea Reyes, Rene |
| author_facet | Fu, Cheng-Hao Lincoln, Andrea Reyes, Rene |
| contents | In this paper we present tight lower-bounds and new upper-bounds for hypergraph and database problems. We give tight lower-bounds for finding minimum hypercycles. We give tight lower-bounds for a substantial regime of unweighted hypercycle. We also give a new faster algorithm for longer unweighted hypercycles. We give a worst-case to average-case reduction from detecting a subgraph of a hypergraph in the worst-case to counting subgraphs of hypergraphs in the average-case. We demonstrate two applications of this worst-case to average-case reduction, which result in average-case lower bounds for counting hypercycles in random hypergraphs and queries in average-case databases. Our tight upper and lower bounds for hypercycle detection in the worst-case have immediate implications for the average-case via our worst-case to average-case reductions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18640 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Worst-Case and Average-Case Hardness of Hypercycle and Database Problems Fu, Cheng-Hao Lincoln, Andrea Reyes, Rene Computational Complexity In this paper we present tight lower-bounds and new upper-bounds for hypergraph and database problems. We give tight lower-bounds for finding minimum hypercycles. We give tight lower-bounds for a substantial regime of unweighted hypercycle. We also give a new faster algorithm for longer unweighted hypercycles. We give a worst-case to average-case reduction from detecting a subgraph of a hypergraph in the worst-case to counting subgraphs of hypergraphs in the average-case. We demonstrate two applications of this worst-case to average-case reduction, which result in average-case lower bounds for counting hypercycles in random hypergraphs and queries in average-case databases. Our tight upper and lower bounds for hypercycle detection in the worst-case have immediate implications for the average-case via our worst-case to average-case reductions. |
| title | Worst-Case and Average-Case Hardness of Hypercycle and Database Problems |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2504.18640 |