【摘要】 在无线传感器网络中,簇首和节点的数量直接关系到整个无线传感器网络的成本及性能,如鲁棒性、容错性等,这也是无线传感器网络设计时首先要考虑的问题。通过把复杂的连通和覆盖问题逐步化简,并利用理论分析、数学建模和几何证明,采用几何理论和数学归纳法的思想,从拓扑学的角度给出了传感器区域的一种网格划分方法。最后从理论上分别给出了在一个实现完全无缝连通和覆盖的传感器区域内最少需要多少簇首和最少需要多少个节点的解析表达式,即从理论上解决了把整个传感器区域至少划分成多少个簇和至少布置多少个节点才能实现完全无缝连通和覆盖的问题。更多还原

【Abstract】 In wireless sensor networks,the number of cluster heads and nodes has direct relation to its cost and its performance,such as robust,fault-tolerance,etc.Further more,it is considered at first as wireless sensor networks are designed.The paper simplifies complex connectivity and coverage problem step by step.By means of theoretical analysis,math modeling and geometry proving and making use of geometric theories and the method of mathematics induction,the method of grid plot of sensor field is proposed from the viewpoints of topology.In the end,the analysis formulae of minimum number of cluster heads and nodes are respectively educed in theory under circumstances of full and seamless connectivity and coverage problem in wireless sensor networks.That is,the problems of full and seamless connectivity and coverage are solved that how many clusters total sensor field is plotted and how many nodes are deployed over the field at the fewest.更多还原