Because wireless sensor networks (WSNs) have been widely used in recent years, how to reduce their energy consumption and interference has become a major issue. Topology control is a common and effective approach to improve network performance, such as reducing the energy consumption and network interference, improving the network connectivity, etc. Many topology control algorithms reduce network interference by dynamically adjusting the node transmission range. However, reducing the network interference by adjusting the transmission range is probabilistic. Therefore, in this paper, we analyze the probability of interference-optimality for the WSNs and prove that the probability of interference-optimality increases with the increasing of the original transmission range. Under a specific transmission range, the probability reaches the maximum value when the transmission range is 0.85 r in homogeneous networks and 0.84 r in heterogeneous networks. In addition, we also prove that when the network is energy-efficient, the network is also interference-optimal with probability 1 both in the homogeneous and heterogeneous networks.
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