{
  "abstract": "We present a significant update to GRAMSCI (GRAph Made Statistics for Cosmological Information; Sabiu et al. 2019), an algorithm for the fast computation of the general $N$-point spatial correlation function of any discrete point set. Version 2 adds several features. We replace the binary-search inner loop ($O(m\\log m)$ per hub-spoke pair, $m$ being the mean neighbor count) with a merge-walk algorithm that reduces the inner loop to $O(m)$. We implement a parity-decomposed 4pCF that separates the signal into even and odd channels. We estimate the disconnected 4pCF internally on the same graph to return the connected 4pCF. We add a Python/NumPy interface to the Fortran engine. Principally, we present a GPU port of the full query engine (OpenACC): the 3pCF, 4pCF, and parity-decomposed 4pCF kernels run on a single consumer GPU with measured speedups of $2.6\\times$ (3pCF) to $9\\times$ (4pCF) over a 64-thread CPU node, and out-of-core tiling handles graphs exceeding device memory. We measure a $9\\times10^9$-edge BAO-scale 3pCF on a 24 GB card with $\\sim 20\\%$ overhead. We validate the code against its CPU reference, against analytic injection tests, and on exactly solvable random fields (a non-Gaussian multiplicative cascade and a Gaussian field, whose full and connected 4pCF the estimators reproduce without bias), and demonstrate BAO-scale applications on the DESI DR1 LRG sample (the 3pCF and the full and connected 4pCF over the complete configuration space, both to 150 $h^{-1}$ Mpc).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.06604",
  "author_total": 1,
  "authors": [
    {
      "name": "Cristiano G. Sabiu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e6x9mc5yw9e81.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.06604",
  "fulltext_url": null,
  "id": "e6x9mc5yw9e81",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.06604",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.CO"
    ],
    [
      "arxiv",
      "astro-ph.IM"
    ],
    [
      "openalex",
      "3103|Galaxies: Formation, Evolution, Phenomena"
    ]
  ],
  "openalex": "W7167829851",
  "pdf_url": "https://arxiv.org/pdf/2607.06604",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e6x9mc5yw9e81.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2607.06604",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.06604"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    },
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.IM",
      "subfield": "instrumentation-methods"
    }
  ],
  "title": "Fast Graph-based Higher-Order Clustering Statistics on the GPU",
  "title_text": "Fast Graph-based Higher-Order Clustering Statistics on the GPU",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:12Z",
  "url": "https://research.draconitic.com/paper/e6x9mc5yw9e81",
  "venue": "arXiv",
  "versions": []
}