在本論文中，我們針對ad-hoc無線感測網路的最糟情形下部署節點問題提出演算法來加以解決。最糟情形下部署節點的問題是指在無線感測區域裡部署新的感測節點來最佳化最糟情形下感測情形。我們找出Maximum breach path與Minimum Delaunay cut之間的對偶關係，並透過這個關係我們提出找出網路Delaunay Cut所形成的防守線以利於部署多個感測節點提升覆蓋率。這個對偶關係產生的結果類似網路最佳化領域中大家熟知的Max-flow-min-cut定理，主要的不同點則是在於我們論文中的目標函數是非線性而不是線性的。基於這個對偶性關係，我們提出一個有效率的對偶性防守線演算法以解決最糟情形下部署節點的問題。另外，我們提出一套基因演算法用來找出多個感測節點部署位置。我們針對提出的定理使用分析證明來解說，並透過模擬結果驗證我們所提出的方法。

In this thesis, we propose and evaluate algorithms for solving the worst-case-coverage deployment problem in ad-hoc wireless sensor networks. The worst-case-coverage deployment problem is to deploy additional sensors in the wireless sensor field to optimize the worst-case coverage. We derive a duality theorem that reveals the close relation between the maximum breach path and the minimum Delaunay cut. The duality theorem is similar to the well-known max-flow-min-cut theorem in the field of network optimization. The major difference lies in the fact that the object function we study in this paper is nonlinear rather than linear. Based on the duality theorem, we propose an efficient dual algorithm to solve the worst-case-coverage deployment problem. In addition, we propose a genetic algorithm for deploying a number of additional sensors simultaneously. We use analytical proofs and simulation results to justify the usage of the proposed approaches.

第一章 緒論 1
1-1無線感測網路的背景 1
1-2 文獻探討 2
1-3 研究動機 4
1-4文章組織 5
第二章 最糟情形覆蓋率下同時多個感測節點部署方案 6
2-1 Voronoi Diagram 6
2-2 MBP (Maximal Breach Path)節點部署 8
2-3 基因演算法(GA)節點部署 11
2-4 GA電腦模擬 16
2-5 防守線(DP)節點部署 25
2-6 DP電腦模擬 33
2-7 模擬結論 36
第三章 結論 37
3-1 總結 37
3-2 未來努力方向 37
參考文獻 38

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