Graph Database Solution for Higher Order Spatial Statistics in the Era of Big Data. (arXiv:1901.00296v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Sabiu_C/0/1/0/all/0/1">Cristiano G. Sabiu</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Hoyle_B/0/1/0/all/0/1">Ben Hoyle</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Kim_J/0/1/0/all/0/1">Juhan Kim</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Li_X/0/1/0/all/0/1">Xiao-Dong Li</a>
We present an algorithm for the fast computation of the general $N$-point We present an algorithm for the fast computation of the general $N$-point http://arxiv.org/icons/sfx.gif
spatial correlation functions of any discrete point set embedded within an
Euclidean space of $mathbb{R}^n$. Utilizing the concepts of kd-trees and graph
databases, we describe how to count all possible $N$-tuples in binned
configurations within a given length scale, e.g. all pairs of points or all
triplets of points with side lengths $
spatial correlation functions of any discrete point set embedded within an
Euclidean space of $mathbb{R}^n$. Utilizing the concepts of kd-trees and graph
databases, we describe how to count all possible $N$-tuples in binned
configurations within a given length scale, e.g. all pairs of points or all
triplets of points with side lengths $<r_{max}$. Through bench-marking we show
the computational advantage of our new graph based algorithm over more
traditional methods. We show that all 3-point configurations up to and beyond
the Baryon Acoustic Oscillation scale ($sim$200 Mpc in physical units) can be
performed on current SDSS data in reasonable time. Finally we present the first
measurements of the 4-point correlation function of $sim$0.5 million SDSS
galaxies over the redshift range $0.43<z<0.7$.
