由於覆蓋問題能反映出感測網路的感測品質，因此它是無線感測網路領域中一個核心的根本問題。許多不同的覆蓋問題相繼的被提出來研究與探討，例如物件覆蓋、面積覆蓋，以及存在障礙物之覆蓋問題。 在這份論文中，我們將研究一個無線感測網路領域中全新且特殊的問題，稱之為(k,ω)-夾角物件覆蓋問題。 我們假設每個感測器的感測範圍都只能夠覆蓋有限的角度與距離，不過感測器能夠自由的旋轉感測的方向，進而覆蓋指定的方向，稱之為有向性感測器。 當分別給定感測器與物件的集合後，我們的目標是使用最少的感測器去(k,ω)-夾角覆蓋最多的物件，使得每個達成覆蓋要求的物件都至少被k個感測器監控，並且感測器彼此與物件之間滿足指定的ω夾角限制。 在這份論文中，為了求取上述問題的最佳解，我們提出了一整數線性規劃方法（Integer Linear Programming; ILP）。 並且為了減低整數線性規劃方法的計算複雜度，我們也提出了一個能保證在最交情況下，所使用的感測器數量不會超過最佳解的四倍的分治近最佳演算法（Divide-and-conquer near-optimal algorithm）。 數值模擬的結果顯示了，與使用有向性感測器的傳統的k-覆蓋策略相比，我們的演算法擁有較佳的正面偵測率。 並且，在夾角限制變的嚴苛時，與貪婪演算法相比，我們的方法也能令更多的物件達到覆蓋要求。

Coverage problem is one of the fundamental problems in wireless sensor networks since it refiects the sensing quality of a sensor network. Various versions of this problem have been studied, such as object, area, and barrier coverage problems. In this thesis, we study a novel coverage problem in a wireless sensor network, called (k, ω)-angle object coverage problem. Each sensor can only cover a limited angle and range, but can freely rotate to any direction to cover a particular angle. Given a set of sensors and a set of objects, our goal is to use the least number of sensors to (k, ω)-angle-cover the largest number of objects such that each object is covered by at least k sensors satisfying an angle constraint ω. In this thesis, we propose an integer linear programming (ILP) approach to finding the optimal solution. To reduce the computation complexity of solving ILP, we present a divide-and-conquer near-optimal algorithm, which guarantees the total number of used sensors does not exceed four times of the optimal solution in worst case. The numerical results show that our algorithms has better facial covering rate of objects than k-cover strategy using directional sensors without angle constraints. And the results also show that the proposed algorithms can be effective in maximizing the ratio of angle-covered objects even if the angle constraint becomes strict.

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