Fast Graph-based Higher-Order Clustering Statistics on the GPU
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(mlog 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× (3pCF) to 9× (4pCF) over a 64-thread CPU node, and out-of-core tiling handles graphs exceeding device memory. We measure a 9×109-edge BAO-scale 3pCF on a 24 GB card with ∼ 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).
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BibTeX
@misc{sabiu2026fast,
title = {{Fast Graph-based Higher-Order Clustering Statistics on the GPU}},
author = {Cristiano G. Sabiu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.06604},
eprint = {2607.06604},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.06604},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fast Graph-based Higher-Order Clustering Statistics on the GPU
AU - Cristiano G. Sabiu
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2607.06604
UR - https://arxiv.org/abs/2607.06604
AB - 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(mlog 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× (3pCF) to 9× (4pCF) over a 64-thread CPU node, and out-of-core tiling handles graphs exceeding device memory. We measure a 9×10^9-edge BAO-scale 3pCF on a 24 GB card with ∼ 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).
ER -