%0 Journal Article
%T A Two-Dimensional Improvement for Farr-Gao Algorithm
%A Tian Dong
%J Mathematics
%D 2010
%I arXiv
%X Farr-Gao algorithm is a state-of-the-art algorithm for reduced Gr\"{o}bner bases of vanishing ideals of finite points, which has been implemented in Maple$^\circledR$ as a build-in command. In this paper, we present a two-dimensional improvement for it that employs a preprocessing strategy for computing reduced Gr\"{o}bner bases associated with tower subsets of given point sets. Experimental results show that the preprocessed Farr-Gao algorithm is more efficient than the classical one.
%U http://arxiv.org/abs/1001.1196v3