  We describe redMaPPer, a new red-sequence cluster finder specifically
designed to make optimal use of ongoing and near-future large photometric
surveys. The algorithm has multiple attractive features: (1) It can iteratively
self-train the red-sequence model based on minimal spectroscopic training
sample, an important feature for high redshift surveys; (2) It can handle
complex masks with varying depth; (3) It produces cluster-appropriate random
points to enable large-scale structure studies; (4) All clusters are assigned a
full redshift probability distribution P(z); (5) Similarly, clusters can have
multiple candidate central galaxies, each with corresponding centering
probabilities; (6) The algorithm is parallel and numerically efficient: it can
run a Dark Energy Survey-like catalog in ~500 CPU hours; (7) The algorithm
exhibits excellent photometric redshift performance, the richness estimates are
tightly correlated with external mass proxies, and the completeness and purity
of the corresponding catalogs is superb. We apply the redMaPPer algorithm to
~10,000 deg^2 of SDSS DR8 data, and present the resulting catalog of ~25,000
clusters over the redshift range 0.08<z<0.55. The redMaPPer photometric
redshifts are nearly Gaussian, with a scatter \sigma_z ~ 0.006 at z~0.1,
increasing to \sigma_z~0.02 at z~0.5 due to increased photometric noise near
the survey limit. The median value for |\Delta z|/(1+z) for the full sample is
0.006. The incidence of projection effects is low (<=5%). Detailed performance
comparisons of the redMaPPer DR8 cluster catalog to X-ray and SZ catalogs are
presented in a companion paper (Rozo & Rykoff 2014).
