# 臺灣博碩士論文加值系統

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 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 -
 [1]R.-S. Ko, An Alternative Theoretical Framework for Analysis of Routing Problems in Wireless Sensor Networks.[2] G. G. Finn, Routing and Addressing Problems in Large Metropolitan- Scale Internetworks, Research ISI/RR-87-180, Information Sciences Institute (March 1987).[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.[4] P. Gupta and P. R. Kumar, "The capacity of wireless networks," Information Theory, IEEE Transactions on, vol. 46, pp. 388-404, 2000.[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 MobileUsing Conjugate Gradient Method for Routing in WSNs- 30 -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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