  The GVW algorithm, presented by Gao et al., is a signature-based algorithm
for computing Gr\"obner bases. In this paper, a variant of GVW is presented.
This new algorithm is called a monomial-oriented GVW algorithm or mo-GVW
algorithm for short. The mo-GVW algorithm presents a new frame of GVW and
regards {\em labeled monomials} instead of {\em labeled polynomials} as basic
elements of the algorithm. Being different from the original GVW algorithm, for
each labeled monomial, the mo-GVW makes efforts to find the smallest signature
that can generate this monomial. The mo-GVW algorithm also avoids generating
J-pairs, and uses efficient methods of searching reducers and checking
criteria. Thus, the mo-GVW algorithm has a better performance during practical
implementations.
