We give a new characterization of the Boolean hierarchy. Our characterization is simple and intuitive, which is based on a single algebraic operator,the symmetric difference, which is commutative and associative.
This paper mainly investigates the connectivity of the unreliable sensor grid network. We consider an unreliable sensor grid network with mn nodes placed in a certain planar area A, and we assume that each node has in...This paper mainly investigates the connectivity of the unreliable sensor grid network. We consider an unreliable sensor grid network with mn nodes placed in a certain planar area A, and we assume that each node has independent failure probability p and has the same transmission range R. This paper presents a new method for calculating the connectivity probability of the network, which uses thorough mathematical methods to derive the relationship among the network connectivity probability, the probability that a node is ＂failed＂ （not active）, the numbers of node, and the node＇s transmission range in unreliable sensor networks. Our approach is more useful and efficient for given problem and conditions. Such as the numerical calculating results indicate that, for a 100×100 size sensot network, if node failure probability is bounded 0.5%, even if the transmission range is small （such as R = 10）, we can still maintain very high connectivity probability （reach 95.8%）. On the other hand, the simulation results show that building high connectivity probability is entirely possible on unreliable sensor grid networks.展开更多
文摘We give a new characterization of the Boolean hierarchy. Our characterization is simple and intuitive, which is based on a single algebraic operator,the symmetric difference, which is commutative and associative.
基金Supported by the National Natural Science Foundation of China(90412012) the Natural Science Foundation of Guangdong Province andthe Post-doctoral Science Foundation of China
文摘This paper mainly investigates the connectivity of the unreliable sensor grid network. We consider an unreliable sensor grid network with mn nodes placed in a certain planar area A, and we assume that each node has independent failure probability p and has the same transmission range R. This paper presents a new method for calculating the connectivity probability of the network, which uses thorough mathematical methods to derive the relationship among the network connectivity probability, the probability that a node is ＂failed＂ （not active）, the numbers of node, and the node＇s transmission range in unreliable sensor networks. Our approach is more useful and efficient for given problem and conditions. Such as the numerical calculating results indicate that, for a 100×100 size sensot network, if node failure probability is bounded 0.5%, even if the transmission range is small （such as R = 10）, we can still maintain very high connectivity probability （reach 95.8%）. On the other hand, the simulation results show that building high connectivity probability is entirely possible on unreliable sensor grid networks.
