無線感測網路(wireless sensor networks, WSNs)的應用很廣，常用在監測/偵測環境。這些應用大部分都有覆蓋(coverage) 的問題。此問題主要就是找尋較少的感測器來偵測事件(event)的發生，且讓感測器覆蓋住所有事件可能發生的地方。通常被監測區域會隨著區域的重要程度，而有不同程度的感測需求。較重要的區域會有較高的感測需求。但大部份的論文，常假設偵測範圍內，每個區域都有相同的重要性。
另外，感測器的感測範圍(sensing range)也常會受到距離的影響，造成感測機率隨著距離增大而降低。在此篇論文中我們採取機率式感測模型(probabilistic detection model)。我們希望使用最少的感測器個數，覆蓋具有不同重要性需求的區域。首先，我們證明用最少感測器來達成完全覆蓋是一個NP-完成性的問題。接著我們提出一個近似(approximation)的演算法來尋找較佳的感測器擺放位置。此外，我們也提出了此一問題理論上需佈置感測器的漸近下限(lower bound)值。從實驗的結果，可以得知我們的方法，找出的感測器個數最差是漸近下限的3倍。

The wireless sensor networks (WSNs) are widely used in many applications to monitor/sense environmental conditions. Most of these applications have the coverage problem. The coverage problem is to place minimal number of sensors which can detect the events in a sensing field. If every point in a sensing field is covered by at least one sensor, the sensing field is full coverage. In the real applications, the sensing requirement of a region depends on the importance of the region. A more important region requires a higher coverage rate or detection probability. However, most of researchers pay less attention to the issue that different regions in a sensing field have different important degrees.
Due to the signal attenuation and noise under realistic environment, the detection probability of a sensor will decrease with increasing its sensing distance. Therefore, we use the probabilistic detection model instead of the binary detection model to solve the coverage problem in which different regions of a sensing field have different important degrees. The region with higher important degree is, the higher event detection probability is required. First, we prove that finding the minimum number of sensors to cover a sensing field with different important regions is NP-complete. Then we propose an approximation algorithm to solve this problem in polynomial time and find the lower bound of this problem. Simulation results show that the solution of our approximation algorithm in the number of sensors is less than three times than the lower bound.

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