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研究生:洪佳鈴
研究生(外文):Hong,Jialing
論文名稱:利用共軛梯度解決無線感測網路路徑
論文名稱(外文):Using Conjugate Gradient Method for Routing in WSNs
指導教授:柯仁松
指導教授(外文):Ko,Rensong
口試委員:柯仁松紀光輝江為國蕭宏章
口試委員(外文):Ko,RensongChi, KuanghuiChiang, WeikuoHsiao, Hungchang
口試日期:2012-07-26
學位類別:碩士
校院名稱:國立中正大學
系所名稱:資訊工程研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:31
中文關鍵詞:無線感測網路高斯賽德爾迭代法共軛梯度演算法
外文關鍵詞:Wireless sensor networkGauss-Seidel algorithmConjugate Gradient method
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  • 被引用被引用:0
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在無線感測網路以宏觀的觀點,去討論繞送路徑,不同於以往圖形的方式,我們考慮整個環境的全域性,利用數值分析將繞送問題描述成偏微分方程式(PDEs),透過有線差分法(FDM)去找到方程式近似解,並從中找出線性方程式。在以Gauss-Seidel Iteration及Conjugate gradient method去解決線性方程式,進而得到負載平衡的繞送路徑。
Conjugate gradient method解偏微分方程式是一種常見迭代方式,是針對特定的線性系統求其解法。一樣以迭代方式解決偏微分方程式的Gauss-Seidel Iteration,再計算的過程中,遇到節點當中密度差距過大的情況,可能會導致無法收斂的問題,Conjugate gradient method可以解決此收斂問題,近似解較為接近實際解,並進而探討密度對整體感測網路佈置節點所造成的影響。
We discuss the routing path from macroscopic view in wireless sensor network, it unlike the previous graphical ways. We consider the whole range with global optimization. The routing problem can be described a partial differential equations (PDEs) by mathematical analysis, then we use finite difference method to find the approximation solution of PDEs, to find the liner equations in the rule. Liner equations can be solved by Gauss-Seidel Iteration and Conjugate gradient method, and we option the routing path for load balance.
Conjugate gradient method is one of common iterative solution on linear system; Gauss-Seidel Iteration is also the method for partial differential equations, when we calculate Gauss-Seidel Iteration, it cannot converge in more variable node density. Conjugate gradient method can solve the convergent problems, and the approximate is close to the actual solution; final we explore the impact of density on disposing sensor node.
第一章 緒論...................................................................................................................... - 6 -
第二章 相關研究 .............................................................................................................. - 9 -
第三章 宏觀分析感測網路 ............................................................................................ - 11 -
3.1 數學描述最佳負載平衡問題 ............................................................................ - 11 -
3.2 有限差分法(finite difference Method) ............................................................ - 13 -
3.3 Gauss-Seidel iteration .......................................................................................... - 14 -
3.4 Distributed Gauss-Seidel iteration ...................................................................... - 15 -
3.5 De la Garza iteration method .............................................................................. - 18 -
3.6 Conjugate Gradient Method ............................................................................... - 18 -
第四章 實驗模擬 ............................................................................................................ - 21 -
4.1 模擬參數設定 .................................................................................................... - 21 -
4.2 誤差值分析 ........................................................................................................ - 21 -
4.3 密度配置 ............................................................................................................ - 24 -
第五章 結論與未來 ........................................................................................................ - 28 -
相關文獻 ............................................................................................................................. - 29 -
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[3] P. Jacquet, "Geometry of information propagation in massively dense ad hoc networks," presented at the Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing, Roppongi Hills, Tokyo, Japan, 2004.
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[5] I. Stojmenovic, X. Lin, Loop-Free Hybrid Single-Path/Flooding Routing Algorithms with Guaranteed Delivery for Wireless Networks, IEEE Trans. Parallel Distrib. Syst. 12 (10) (2001) 1023–1032.
[6] I. Stojmenovic, M. Russell, B. Vukojevic, Depth First Search and Location Based Localized Routing and QoS Routing in Wireless Networks, in: Proceedings of the 2000 International Conference on Parallel Processing, IEEE Computer Society, Toronto, Canada, 2000, pp. 173–180.
[7] T. He, J. A. Stankovic, C. Lu, T. Abdelzaher, SPEED: A Stateless Protocol for Real-Time Communication in Sensor Networks, in: Proceedings of the 23rd International Conference on Distributed Computing Systems, IEEE Computer Society, Providence, Rhode Island, USA, 2003.
[8] B. Karp, H. T. Kung, GPSR: Greedy Perimeter Stateless Routing for Wireless Networks, in: Proceedings of the 6th Annual International Conference on Mobile
Using Conjugate Gradient Method for Routing in WSNs
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Computing and Networking, ACM, Boston, MA, US, 2000, pp. 243–254.
[9] R. Catanuto and G. Morabito, "Optimal Routing in Dense Wireless Multihop Networks as a Geometrical Optics Solution to the Problem of Variations," in Communications, 2006. ICC '06. IEEE International Conference on, 2006, pp. 134-139.
[10] R. Catanuto, et al., "Optical/Optimal Routing in Massively Dense Wireless Networks," in INFOCOM 2007. 26th IEEE International Conference on Computer Communications. IEEE, 2007, pp. 1010-1018.
[11] R. Catanuto, et al., "On asymptotically optimal routing in large wireless networks and Geometrical Optics analogy," Computer Networks, vol. 53, pp. 1939-1955, 2009.
[12] M. Kalantari, M. Shayman, Design Optimization of Multi-Sink Sensor Networks by Analogy to Electrostatic Theory, in: Proceedings of IEEE Wireless Communications and Networking Conference, Las Vegas, NV USA,
[13]J. E. Marsden, A. J. Tromba, Vector Calculus, 5th Edition, W. H. Freeman,2003.
[14] R.-S. Ko, "Analyzing the Redeployment Problem of Mobile Wireless Sensor Networks via Geographic Models," Wireless Communications and Mobile Computing, 2011
[15] R.-S. Ko, "Macroscopic Analysis of Wireless Sensor Network Routing Problems," 2011.
[16] G.H. Golub, C.F. Van Loan, Matrix Computations, third ed., The Johns Hopkins University Press, 1996.
[17] R.-S. Ko, "A distributed routing algorithm for sensor networks derived from macroscopic models," Computer Networks, vol. 55, pp. 314-329, 2011.
Using Conjugate Gradient Method for Routing in WSNs
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