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We present an algorithm that computes the multipole coefficients of thegalaxy three-point correlation function (3PCF) without explicitly consideringtriplets of galaxies. Rather, centering on each galaxy in the survey, itexpands the radially-binned density field in spherical harmonics and combinesthese to form the multipoles without ever requiring the relative angle betweena pair about the central. This approach scales with number and number densityin the same way as the two-point correlation function, allowing runtimes thatare comparable, and 500 times faster than a naive triplet count. It is exact inangle and easily handles edge correction. We demonstrate the algorithm on theLasDamas SDSS-DR7 mock catalogs, computing an edge corrected 3PCF out to$90\;{\rm Mpc}/h$ in under an hour on modest computing resources. We expectthis algorithm will render it possible to obtain the large-scale 3PCF forupcoming surveys such as Euclid, LSST, and DESI.

Computing the Three-Point Correlation Function of Galaxies in $\mathcal{O}(N^2)$ Time