  We outline here the next generation of cluster-finding algorithms. We show
how advances in Computer Science and Statistics have helped develop robust,
fast algorithms for finding clusters of galaxies in large multi-dimensional
astronomical databases like the Sloan Digital Sky Survey (SDSS). Specifically,
this paper presents four new advances: (1) A new semi-parametric algorithm -
nicknamed ``C4'' - for jointly finding clusters of galaxies in the SDSS and
ROSAT All-Sky Survey databases; (2) The introduction of the False Discovery
Rate into Astronomy; (3) The role of kernel shape in optimizing cluster
detection; (4) A new determination of the X-ray Cluster Luminosity Function
which has bearing on the existence of a ``deficit'' of high redshift, high
luminosity clusters. This research is part of our ``Computational
AstroStatistics'' collaboration (see Nichol et al. 2000) and the algorithms and
techniques discussed herein will form part of the ``Virtual Observatory''
analysis toolkit.
