different cluster observables are used. The first is the bi-weighted velocity dispersion and the second is the summed optical luminosity of the galaxies within the cluster. To calculate the velocity dispersion ($\sigma_v$), an iterative technique is performed using the robust bi-weighted statistics of Beers et al. (1990). The total optical luminosity of the clusters is determined by converting the apparent magnitudes of galaxies in the cluster to optical luminosities using the conversions in Fukugita et al. (1996). All magnitudes are also $k$-corrected according to Blanton et al. (2002) and extinction corrected according to Schlegel, Finkbeiner, and Davis (1998). Cluster membership is defined to be any galaxy within $4\sigma_v$ in redshift, and within $1.5h^{-1}Mpc$ projected separation on the sky. For the halo catalog, the mass within 200 times the critical density ($M_{200}$) is used as determined from summing up all the dark matter particles within this radius around each halo ($R_{200}$; see Evrard et al. 2002).

### Purity and Completeness: Challenges One and Two {#purity}

The C4 algorithm has been applied to these mock SDSS galaxy catalogs. In Figure \[completeness\], I show the purity of the matched C4 clusters found in the simulation as a function of the total $r$ band 