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Finding Hypercliques Faster Than Brute Force — arXiv:2611.05082

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.05082
License (as archived): CC0-1.0
Archived: 2026-11-04T19:07:43.790Z
SHA-256 of the archived text: 5a2c0f16607587a77e0a0b808188f84836d6d57aeebb7e25e79301926423c8da
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How to cite

Finding Hypercliques Faster Than Brute Force — arXiv:2611.05082 — arXiv (en), https://arxiv.org/abs/2611.05082 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bfdf59ddaf4f (Metraipolis archive dc_bfdf59ddaf4f, sha256 5a2c0f16607587a77e0a0b808188f84836d6d57aeebb7e25e79301926423c8da)

BibTeX

@misc{dcbfdf59ddaf4f,
  title = {Finding Hypercliques Faster Than Brute Force — arXiv:2611.05082},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.05082},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bfdf59ddaf4f; sha256 5a2c0f16607587a77e0a0b808188f84836d6d57aeebb7e25e79301926423c8da},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.05082. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We show that for any fixed $k$, there exists $\varepsilon_k > 0$ such that, given a $(k-1)$-uniform hypergraph $H$ on $n$ vertices, one can count the number of $k$-hypercliques in $H$ in $O(n^{k-\varepsilon_k})$ time. This refutes the hyperclique conjecture of Lincoln, Vassilevska Williams, and Williams (SODA 2018). Our result follows from the uniform construction of a family of arithmetic circuits of size $O(n^{k-\varepsilon_k})$ for the $k$-hyperclique tensor, a natural higher-order generalization of the matrix multiplication tensor. We obtain two corollaries. First, for every $k$, there exists $\varepsilon > 0$ such that Max-$k$SAT can be solved in $2^{(1-\varepsilon)n} \cdot \mathrm{poly}(m,n)$ time. Second, for every $k$, there exists $\varepsilon > 0$ such that arithmetic progressions of length $k$ in subsets of $\{0,1,\ldots,n\}$ can be detected in $n^{2-\varepsilon}$ time. Both corollaries refute other prominent conjectures in the literature.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv cs.DS, nuovi lavori del giorno).
Categorie arXiv: Data Structures and Algorithms (cs.DS) ; Computational Complexity (cs.CC).
Pagina del lavoro: https://arxiv.org/abs/2611.05082 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-04T18:40:52.481Z dalla pagina https://arxiv.org/list/cs.DS/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).