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We present a comparison of three cluster finding algorithms from imaging datausing Monte Carlo simulations of clusters embedded in a 25 deg^2 region ofSloan Digital Sky Survey (SDSS) imaging data: the Matched Filter (MF; Postmanet al. 1996), the Adaptive Matched Filter (AMF; Kepner et al. 1999) and acolor-magnitude filtered Voronoi Tessellation Technique (VTT). Among the twomatched filters, we find that the MF is more efficient in detecting faintclusters, whereas the AMF evaluates the redshifts and richnesses moreaccurately, therefore suggesting a hybrid method (HMF) that combines the two.The HMF outperforms the VTT when using a background that is uniform, but it ismore sensitive to the presence of a non-uniform galaxy background than is theVTT; this is due to the assumption of a uniform background in the HMF model. Wethus find that for the detection thresholds we determine to be appropriate forthe SDSS data, the performance of both algorithms are similar; we present theselection function for each method evaluated with these thresholds as afunction of redshift and richness. For simulated clusters generated with aSchechter luminosity function (M_r^* = -21.5 and alpha = -1.1) both algorithmsare complete for Abell richness >= 1 clusters up to z ~ 0.4 for a samplemagnitude limited to r = 21. While the cluster parameter evaluation shows amild correlation with the local background density, the detection efficiency isnot significantly affected by the background fluctuations, unlike previousshallower surveys.Comment: 38 pages, 15 figures, Accepted for publication in A

Detecting Clusters of Galaxies in the Sloan Digital Sky Survey. I. Monte Carlo Comparison of Cluster Detection Algorithms