在無線網感測網路研究中，佈置感測節點是一重要的議題。因為選用一個最佳化感測節點佈建模式，使得需要佈建的感測節點數量最少，降低無線網路應用的成本。而現有的研究中，僅提出在部分k 值(k<=25)的最佳化k 連接性(connectivity)三維感測網路的節點佈建模式，卻並未提出一個系統性的方法來決定在任意正整數k 時最佳化k 連接性(connectivity)的佈建圖形。 本篇研究中，假設感測節點都是均質，並以對稱之方式擺放在一個很大的空間裡。因此，由每個感測節點所組成的范諾圖(Voronoi diagram)會是立方體及菱形十二面體，這兩種對稱的空間填充凸多面體(space-filling convex polyhedra)其中一種。基於這個假設，本研究設計一套搜尋的演算法Bound and Search (BS)， 計算在滿足k 連接性(connectivity)的無線感測網路下，感測節點所需的傳輸半徑。藉由比較立方體及菱形十二面體這兩種感測節點佈建模式之下，達到k 連接性(connectivity)時，感測節點所需的傳輸半徑及感測節點密度這兩個數據，本研究的演算法可以找到一個在三維無線感測網路下，最佳化的k 連接佈建圖形。此外，實驗結果顯示，除了在比較小範圍的k 值( 15 <= k <= 25 )，採用菱形十二面體的節點佈建模式，所需個節點密度較正立方體的節點佈建模式小。;To reduce the operational cost of wireless sensor networks, nding the optimal deployment pattern to achieve a given connectivity requirement with the minimum number of sensor nodes is important. Although the optimal k-connectivity deployment pattern (k<=25) for 3-D wireless sensor networks have been studied, there is yet to have a general framework in identifying the optimal k-connectivity deployment pattern for an arbitrary k value. In this thesis, we assume that sensor nodes are homogeneous and deployed over an very large area symmetrically. As a result, the Voronoi diagram of sensor nodes will be one of the symmetric space- lling convex polyhedra, i.e., cube and rhombic dodecahedron. An algorithm, called Bound and Search (BS), is proposed to compute the transmission radius required for sensor nodes to achieve k connectivity. By comparing the transmission radius and node density resulted from the cube and rhombic dodecahedron patterns, our algorithm is able to discovers the optimal k-connectivity deployment pattern in 3-D wireless sensor networks. Moreover, our results indicate that, other than a small range of k (i.e., 15 <= k <= 25 ), the rhombic dodecahedron pattern requires a smaller node density to achieve the same k-connectivity requirement when compared with the cube pattern.
