A two-dimensional improvement for Farr-Gao algorithm

Farr-Gao algorithm is a state-of-the-art algorithm for reduced Gröbner bases of vanishing ideals of finite points, which has been implemented in Maple as a build-in command. This paper presents a two-dimensional improvement for it that employs a preprocessing strategy for computing reduced Gröbner 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.