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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. [ABSTRACT FROM AUTHOR]

The construction of X-ray cluster surveys is described. As an example the selection processes applied to the REFLEX survey and first results of an analysis of the spatial distributions of the clusters are given in more detail. [ABSTRACT FROM AUTHOR]

The cosmologically most important cluster parameter is its gravitational mass. In order to constrain cosmological models of structure formation by comparing simulations or analytic models with, e.g., observational mass functions of statistical cluster samples, cluster masses are needed. Precise cluster mass determinations for large cluster surveys, e.g. [3], however, require extensive observations and are currently not feasible. An alternative approach is to use established relations between more easily observed quantities and cluster mass. For optical cluster samples the observed number of cluster galaxies has sometimes been used to relate to cluster mass. For X-ray cluster samples a three component approach is commonly used. First, measured X-ray luminosities are converted to X-ray temperatures using an observational relation. Then, a slope for the X-ray temperature - gravitational mass relation is assumed on theoretical grounds. And finally, the X-ray temperatures are converted to masses by normalizing this relation with hydrodynamical simulations. [ABSTRACT FROM AUTHOR]