Computer-implemented systems and methods are provided for reducing a number of options presented to a user where the options have characteristics that are arranged in a multi-dimensional hierarchical space. A system and method can be configured to identify common dimensions using dimension nodes in dimensional points and identify compatible nodes for each dimension in the multi-dimensional hierarchical space by determining whether an association exists. Compatible pairs of surviving points are generated after applying each of the compatible nodes from the common dimensions. Greatest lower bounds (GLBs) are computed for each of the generated compatible points, and a set of options is generated comprising points from the generated compatible points and the computed GLBs.