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This paper is the first in a series, presenting a new galaxy cluster finder based on a three-dimensional Voronoi Tesselation plus a maximum likelihood estimator, followed by gapping-filtering in radial velocity(VoML+G). The scientific aim of the series is a reassessment of the diversity of optical clusters in the local universe. A mock galaxy database mimicking the southern strip of the magnitude(blue)-limited 2dF Galaxy Redshift Survey (2dFGRS), for the redshift range 0.009 N g ≥ 5, and 14% with N g < 5. The ensemble of VoML+G clusters has a ~59% completeness and a ~66% purity, whereas the subsample with N g ≥ 10, to z ~ 0.14, has greatly improved mean rates of ~75% and ~90%, respectively. The VoML+G cluster velocity dispersions are found to be compatible with those corresponding to "Millennium clusters" over the 300–1000 km s−1 interval, i.e., for cluster halo masses in excess of ~3.0 × 1013 M ⊙ h −1.

A 3D Voronoi+Gapper Galaxy Cluster Finder in Redshift Space toz∼ 0.2 I: an Algorithm Optimized for the 2dFGRS