Energy balance consumption is an important research topic in the field of wireless sensor networks (WSNs). Clustering protocols are widely used to reduce WSN energy consumption. However, this many-to-one cluster head (CH) model can also easily lead to energy exhaustion of some critical nodes near the base station results in the decline of the network quality and lifetime. This article proposes a clustering election game-based and two-level management clustering protocol (CEGT) for WSNs; the network is divided into layers of equal size, and the layer heads (LHs) are selected within the layers based on the location and energy information. Each layer is further divided into clusters of equal size, and the nodes within the clusters undergo a two-stage screening followed by local clustering and multiple rounds of election games to dynamically select the staged CHs. This protocol effectively prevents low-energy nodes from participating in the CH competitions, and selects high-quality nodes through election games which are based on customized qualification values, and ensures reasonable energy utilization as well as efficient network load balancing. Finally, our simulations show that our CEGT protocol outperforms other clustering protocols in terms of the network lifetime, the number of surviving nodes, and the average number of clusters, and the throughput, which also indicate that the CEGT protocol is more suitable for large-scale networks.

This paper discusses two classes of symmetric Boolean functions. For each class, a necessary and sufficient condition for having optimum algebraic immunity is proposed. The algebraic degree and nonlinearity of the Boolean functions are also completely determined. And then we prove several of Braeken's conjectures about the algebraic degree and nonlinearity of the Boolean functions with optimum algebraic immunity in the two classes.

This paper provides a fast algorithm for Gröbner bases of ideals of F[x, y] over a field F. We show that only the S-polynomials of neighbor pairs of a strictly ordered finite generating set are needed in the computing of a Gröbner bases of the ideal. It reduces dramatically the number of unnecessary S-polynomials that are processed. Although the complexity of the algorithm is hard to evaluated, it obviously has a great improvement from Buchberger's Algorithm.