29,301 research outputs found
An Improvement over the GVW Algorithm for Inhomogeneous Polynomial Systems
The GVW algorithm is a signature-based algorithm for computing Gr\"obner
bases. If the input system is not homogeneous, some J-pairs with higher
signatures but lower degrees are rejected by GVW's Syzygy Criterion, instead,
GVW have to compute some J-pairs with lower signatures but higher degrees.
Consequently, degrees of polynomials appearing during the computations may
unnecessarily grow up higher and the computation become more expensive. In this
paper, a variant of the GVW algorithm, called M-GVW, is proposed and mutant
pairs are introduced to overcome inconveniences brought by inhomogeneous input
polynomials. Some techniques from linear algebra are used to improve the
efficiency. Both GVW and M-GVW have been implemented in C++ and tested by many
examples from boolean polynomial rings. The timings show M-GVW usually performs
much better than the original GVW algorithm when mutant pairs are found.
Besides, M-GVW is also compared with intrinsic Gr\"obner bases functions on
Maple, Singular and Magma. Due to the efficient routines from the M4RI library,
the experimental results show that M-GVW is very efficient
A Monomial-Oriented GVW for Computing Gr\"obner Bases
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
Link Prediction Based on Common-Neighbors for Dynamic Social Network
AbstractLink prediction is an important issue in social networks. Most of the existing methods aim to predict interactions between individuals for static networks, ignoring the dynamic feature of social networks. This paper proposes a link prediction method which considers the dynamic topology of social networks. Given a snapshot of a social network at time t (or network evolution between t1 and t2), we seek to accurately predict the edges that will be added during the interval from time t (or t2) to a given future time t′. Our approach utilizes three metrics, the time-varied weight, the change degree of common neighbor and the intimacy between common neighbors. Moreover, we redefine the common neighbors by finding them within two hops. Experiments on DBLP show that our method can reach better results
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