无线传感器网络节能策略研究
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摘要
随着网络技术和微机电系统技术的进步,以较低花费部署一组网络机器人于大范围内自动监测与收集数据是可行的。这些机器人以ad-hoc网络方式共享其感测信息,并通过协作与自适应配置构成了以监测指定环境为任务的无线传感器网络。
无线传感器网络在军用与民用上均具有广泛的用途,例如战场搜救、危险环境操作、环境监测、目标跟踪和远程感测。
无线传感器网络中的节点一般采用电池供电,可以使用的电量非常有限,而更换电池是困难的甚至是不可能的;但是无线传感器网络的生存时间却要求长达数月甚至数年。因此,如何在不影响功能的前提下,尽量节约无线传感器网络的电池能量成为无线传感器网络的核心问题,也是当前国内外研究机构关注的焦点。
本文的目的是设计与验证无线传感器网络的节能方法。本文重点研究了几个与无线传感器网络及其能耗有关的问题。
本文基于图论与机器人运动学,针对无线传感器网络分布式协作与多跳通信特点,提出了一种动态模型。该模型用Delaunay三角剖分和Voronoi图描述相邻节点的几何关系。模型中,每个节点的行为只与其一跳相邻节点和其所处环境有关。该模型为无线传感器网络中各种任务(例如网络的自组织覆盖,网络数据查询路由,相邻节点的信息共享)的完成提供了一个解决方案。
为解决无线传感器网络连接与覆盖问题,本文提出了三种自组织算法。第一种方法利用微粒群算法在多目标优化方面的优势,用其改善传感器网络节点的自组织,使得网络在覆盖的均匀性、快速性和连结的可靠性方面均有较好的表现。第二种方法是一种虚拟力与粒子群相结合的分布式自组织算法。在虚拟力方法中引力与斥力共同作用,控制着网络的自组织过程,其系数的确定与传感器网络展开的效果密切相关。此算法先用改进型粒子群算法对引力系数与斥力系数寻优,然后利用这两个系数的寻优结果计算出虚拟力并部署节点。仿真表明此方法能够兼顾部署的快速性和最终的覆盖率。第三种方法将市场竞争规律应用于无线传感器网络的连接与覆盖,把传感器网络中的节点类比为市场竞争中的经济主体,把目标监测区域类比为经济资源,把对传感器网络所做的优化配置类比为市场竞争行为对经济资源的优化配置。该算法能够降低节点的计算量、移动距离及信息复杂度,也能提高网络的节能效率。
针对无线传感器网络多跳转播问题,本文根据Friis自由空间方程推导出使用中继节点通信能够减少能耗的必要条件,提出了一种能量高效性单播路由算法。该算法首先对被讨论的网络剪枝,只保留满足节能条件的中继节点。剪枝后的网络被看作一个图,在给每一跳赋一个反映其能耗的代价值后可以计算出最小代价路径。仿真结果表明该算法在节省能量和算法复杂度方面能够取得较好的平衡,同时也体现了将剪枝应用于无线传感器网络的优越性和潜力。
为降低无线传感器网络中射频模块的能量消耗,本文提出了一种基于指向性天线的节能策略。该方法利用指向性天线的高增益、低旁瓣特性,能够大量减少信道损失、冲突、串扰等因素引起的能耗,显著提高网络的能量利用效率。
基于Delaunay三角剖分和Voronoi图,本文提出了一种数据融合方法,并结合本文提出的能耗模型对其节能原理做了分析。仿真结果表明将数据融合方法应用于无线传感器网络节能是有效的。
在全文的结论部分,归纳了本文所做的主要工作和仍然存在的几点不足,并对无线传感器网络节能策略研究的发展趋势做了展望。
With the technology advances in networking and electro-mechanical systems, it is now practical and relatively inexpensive to deploy a group of networked robots for autonomous sensing and data collection in a broad area. These robots sense the environment with onboard sensors and share sensory information through an ad-hoc wireless network. The vehicle group cooperatively performs tasks as a wireless sensor network, which adapts its configuration and coordination behaviors in response to the sensed environment.
Wireless sensor networks may find myriad of civilian and military applications, such as battlefield surveillance, search and recovery operations, manipulation in hazardous environments, environment monitoring, target tracking and remote sensing.
Generally, sensors in wireless sensor networks battery-powered, their energy is severely limited. But the replacement of the battery is difficult or even impossible and the survival time of wireless sensor networks have to last several months or even several years. Therefore, saving battery energy as far as possible under the premise of quality of service is the core issue and the focus.
The objective of this paper is to develop and experimentally verify methodologies for reducing energy-cost of wireless sensor networks. The proposed project investigates several fundamental problems associated with wireless sensor networks and their energy-cost.
Based on graph theory and robot kinematics, a dynamic model for the distributed cooperation and multi-hop communication of wireless sensor networks has been proposed. Delaunay triangulation and Voronoi diagram are introduced to model the geometrical relationship between neighboring mobile robots, where the motion of a robot is only related to its immediate one-hop neighbors and its environment. The distributed dynamic model provide a paradigm for the development of a variety of sensor network tasks, such as self-deployment for maximizing coverage area, data routing for querying the network, information sharing between neighboring sensors.
Three kinds of self-deployment algorithms for the connectivity and coverage of sensor networks have been developed. The first method improves the self-deployment of sensor networks by means of PSO algorithm. Satisfied performances in terms of coverage uniformity, coverage speed and link reliability have been obtained due to optimized capacity of PSO for multiple targets. In the second method, virtual potential field method is combined with the particle swarm optimization algorithm develop distributed autonomous deployment algorithms for wireless sensor networks. In virtual potential field method, attractive and repulsive forces control the self-deployment process of mobile sensor network together. The values of their coefficients are relative to spreading out effect of the networks. The coefficients are optimized by means of improved particle swarm optimization algorithm. With the optimization results, virtual forces are calculated and sensors are deployed. The simulation results show that this method makes sensors deployment fast and with high coverage percentage. The third method applies the market competition law to connectivity and coverage of wireless sensor networks. In this algorithm, the sensor nodes in the network were seen as enterprises in economic activities, the interested areas were seen as resources, network configurations were seen as market competitions. Take advantage of this algorithm, the amount of computation, mobile distance and information complexity of every sensor can be reduced. The efficiency of energy-saving has been boost indirectly in these projects. Experimental results show that this method is effective.
In order to solve multi-hop forwarding problems in wireless sensor networks, a necessary condition about reducing energy consume by means of relay communications has been deduced from Friis free-space equation, and an energy efficient unicast routing algorithm has been proposed. This algorithm adopt the following steps: the interested network has been prune first, only the relay sensors which can reduce path loss remained, the pruned network is seen as a graph, conferred to each hop a value according to its energy consumption and find the least cost path. Simulation results indicate the algorithm achieves satisfactory balance between saving energy and complexity, and show the superiority and potential of pruning in wireless sensor networks.
An energy-saving strategy based on directional antenna has been proposed to reduce energy consumption of RF module in wireless sensor networks. Taking advantage of directional antennas with high gains and low side-lobes, in this method, the energy consumption from path loss, collisions and overhearing have been reduced greatly and the efficiency of energy can be improved greatly.
Based on Delaunay triangulation and Voronoi diagram, an information fusions method has been proposed to reduce the energy-cost of data transmission in wireless sensor networks. With the energy consumption model proposed in this paper, the energy-saving reasons of this method have been discussed. Simulation results show information fusions in wireless sensor networks are of good effect of energy-saving.
Finally, we summarize our achievements and limitations, and then make an expectation on future research of wireless sensor networks’energy-saving strategies at the last part of the thesis.
无线传感器网络在军用与民用上均具有广泛的用途,例如战场搜救、危险环境操作、环境监测、目标跟踪和远程感测。
无线传感器网络中的节点一般采用电池供电,可以使用的电量非常有限,而更换电池是困难的甚至是不可能的;但是无线传感器网络的生存时间却要求长达数月甚至数年。因此,如何在不影响功能的前提下,尽量节约无线传感器网络的电池能量成为无线传感器网络的核心问题,也是当前国内外研究机构关注的焦点。
本文的目的是设计与验证无线传感器网络的节能方法。本文重点研究了几个与无线传感器网络及其能耗有关的问题。
本文基于图论与机器人运动学,针对无线传感器网络分布式协作与多跳通信特点,提出了一种动态模型。该模型用Delaunay三角剖分和Voronoi图描述相邻节点的几何关系。模型中,每个节点的行为只与其一跳相邻节点和其所处环境有关。该模型为无线传感器网络中各种任务(例如网络的自组织覆盖,网络数据查询路由,相邻节点的信息共享)的完成提供了一个解决方案。
为解决无线传感器网络连接与覆盖问题,本文提出了三种自组织算法。第一种方法利用微粒群算法在多目标优化方面的优势,用其改善传感器网络节点的自组织,使得网络在覆盖的均匀性、快速性和连结的可靠性方面均有较好的表现。第二种方法是一种虚拟力与粒子群相结合的分布式自组织算法。在虚拟力方法中引力与斥力共同作用,控制着网络的自组织过程,其系数的确定与传感器网络展开的效果密切相关。此算法先用改进型粒子群算法对引力系数与斥力系数寻优,然后利用这两个系数的寻优结果计算出虚拟力并部署节点。仿真表明此方法能够兼顾部署的快速性和最终的覆盖率。第三种方法将市场竞争规律应用于无线传感器网络的连接与覆盖,把传感器网络中的节点类比为市场竞争中的经济主体,把目标监测区域类比为经济资源,把对传感器网络所做的优化配置类比为市场竞争行为对经济资源的优化配置。该算法能够降低节点的计算量、移动距离及信息复杂度,也能提高网络的节能效率。
针对无线传感器网络多跳转播问题,本文根据Friis自由空间方程推导出使用中继节点通信能够减少能耗的必要条件,提出了一种能量高效性单播路由算法。该算法首先对被讨论的网络剪枝,只保留满足节能条件的中继节点。剪枝后的网络被看作一个图,在给每一跳赋一个反映其能耗的代价值后可以计算出最小代价路径。仿真结果表明该算法在节省能量和算法复杂度方面能够取得较好的平衡,同时也体现了将剪枝应用于无线传感器网络的优越性和潜力。
为降低无线传感器网络中射频模块的能量消耗,本文提出了一种基于指向性天线的节能策略。该方法利用指向性天线的高增益、低旁瓣特性,能够大量减少信道损失、冲突、串扰等因素引起的能耗,显著提高网络的能量利用效率。
基于Delaunay三角剖分和Voronoi图,本文提出了一种数据融合方法,并结合本文提出的能耗模型对其节能原理做了分析。仿真结果表明将数据融合方法应用于无线传感器网络节能是有效的。
在全文的结论部分,归纳了本文所做的主要工作和仍然存在的几点不足,并对无线传感器网络节能策略研究的发展趋势做了展望。
With the technology advances in networking and electro-mechanical systems, it is now practical and relatively inexpensive to deploy a group of networked robots for autonomous sensing and data collection in a broad area. These robots sense the environment with onboard sensors and share sensory information through an ad-hoc wireless network. The vehicle group cooperatively performs tasks as a wireless sensor network, which adapts its configuration and coordination behaviors in response to the sensed environment.
Wireless sensor networks may find myriad of civilian and military applications, such as battlefield surveillance, search and recovery operations, manipulation in hazardous environments, environment monitoring, target tracking and remote sensing.
Generally, sensors in wireless sensor networks battery-powered, their energy is severely limited. But the replacement of the battery is difficult or even impossible and the survival time of wireless sensor networks have to last several months or even several years. Therefore, saving battery energy as far as possible under the premise of quality of service is the core issue and the focus.
The objective of this paper is to develop and experimentally verify methodologies for reducing energy-cost of wireless sensor networks. The proposed project investigates several fundamental problems associated with wireless sensor networks and their energy-cost.
Based on graph theory and robot kinematics, a dynamic model for the distributed cooperation and multi-hop communication of wireless sensor networks has been proposed. Delaunay triangulation and Voronoi diagram are introduced to model the geometrical relationship between neighboring mobile robots, where the motion of a robot is only related to its immediate one-hop neighbors and its environment. The distributed dynamic model provide a paradigm for the development of a variety of sensor network tasks, such as self-deployment for maximizing coverage area, data routing for querying the network, information sharing between neighboring sensors.
Three kinds of self-deployment algorithms for the connectivity and coverage of sensor networks have been developed. The first method improves the self-deployment of sensor networks by means of PSO algorithm. Satisfied performances in terms of coverage uniformity, coverage speed and link reliability have been obtained due to optimized capacity of PSO for multiple targets. In the second method, virtual potential field method is combined with the particle swarm optimization algorithm develop distributed autonomous deployment algorithms for wireless sensor networks. In virtual potential field method, attractive and repulsive forces control the self-deployment process of mobile sensor network together. The values of their coefficients are relative to spreading out effect of the networks. The coefficients are optimized by means of improved particle swarm optimization algorithm. With the optimization results, virtual forces are calculated and sensors are deployed. The simulation results show that this method makes sensors deployment fast and with high coverage percentage. The third method applies the market competition law to connectivity and coverage of wireless sensor networks. In this algorithm, the sensor nodes in the network were seen as enterprises in economic activities, the interested areas were seen as resources, network configurations were seen as market competitions. Take advantage of this algorithm, the amount of computation, mobile distance and information complexity of every sensor can be reduced. The efficiency of energy-saving has been boost indirectly in these projects. Experimental results show that this method is effective.
In order to solve multi-hop forwarding problems in wireless sensor networks, a necessary condition about reducing energy consume by means of relay communications has been deduced from Friis free-space equation, and an energy efficient unicast routing algorithm has been proposed. This algorithm adopt the following steps: the interested network has been prune first, only the relay sensors which can reduce path loss remained, the pruned network is seen as a graph, conferred to each hop a value according to its energy consumption and find the least cost path. Simulation results indicate the algorithm achieves satisfactory balance between saving energy and complexity, and show the superiority and potential of pruning in wireless sensor networks.
An energy-saving strategy based on directional antenna has been proposed to reduce energy consumption of RF module in wireless sensor networks. Taking advantage of directional antennas with high gains and low side-lobes, in this method, the energy consumption from path loss, collisions and overhearing have been reduced greatly and the efficiency of energy can be improved greatly.
Based on Delaunay triangulation and Voronoi diagram, an information fusions method has been proposed to reduce the energy-cost of data transmission in wireless sensor networks. With the energy consumption model proposed in this paper, the energy-saving reasons of this method have been discussed. Simulation results show information fusions in wireless sensor networks are of good effect of energy-saving.
Finally, we summarize our achievements and limitations, and then make an expectation on future research of wireless sensor networks’energy-saving strategies at the last part of the thesis.
引文
[1]王蓓,孟伟民.无线传感器网络在信息战中的运用探讨[J].中国科技信息, 2005, (23): 44.
[2]牟连佳,牟连泳.无线传感网络及其在工业领域应用研究[J].工业控制计算机, 2005, 18(1):3-5.
[3]乔晓军,张馨,王成等.无线传感器网络在农业中的应用[J].农业工程学报, 2005, 21 (12):232-234.
[4]马碧春.无线传感器网络在医疗行业的应用展望[J].中国医院管理, 2006, 26(10):73.
[5]田欣,胡莲.基于无线传感网的城市应急指挥系统关键技术初探[J].经济师, 2006, (6): 53-54.
[6]饶云华,代莉,赵存成等.基于无线传感器网络的环境监测系统[J].武汉大学学报(理学版), 2006, 52(3):345-348.
[7]李光辉,赵军,王智.基于无线传感器网络的森林火灾监测预警系统[J].传感技术学报, 2006, 19(6):2761-2764.
[8]李莹莹,刘云辉,樊玮虹等.基于移动通信网络的机器人遥操作[J].通信学报, 2006, 27 (5):52-59.
[9]张志海,沈连丰,叶芝慧等.一种基于Zigbee的无线传感器网络教学实验系统[J].电气电子教学学报, 2006, 28(5):76-80.
[10]吴成东,郑君刚,刘大任等.基于无线传感器网络的智能家居网络技术研究[J].沈阳建筑大学学报, 2005, 21(6):753-756.
[11] Leonard J, Durrant-Whyte H. Mobile robot localization by tracking geometric beacons[J]. IEEE Transactions on Robotics and Automation, 1991, 7(3):376-382.
[12] Guivant J, Nebot E. Optimization of the simultaneous localization and map-building alg- orithm for real-time implementation[J]. IEEE Transactions on Robotics and Automation, 2001, 17(3):242-257.
[13] Fox D, Burgard W, Kruppa H. A probabilistic approach to collaborative multi-robot loca- lization[J]. Autonomous Robots, 2000, 8(3):325-344.
[14] Thrun S, Fox D, Burgard W, et al. Robust Monte Carlo localization for mobile robots art- ificial intelligence[J]. Artificial Intelligence, 2000, 128(1):99-141.
[15]刘丽萍,王智,孙优贤.无线传感器网络部署及其覆盖问题研究[J].电子与信息学报, 2006, 28(9):1752-1757.
[16] Akyildiz IF, Su W, Sankarasubramaniam Y, et al. Wireless sensor networks: a survey[J]. Computer Networks, 2002, 38(4):393-422.
[17] Iyengar SS, Kumar S. Preface of special issue on distributed sensor networks[J]. The International Journal of High Performance Computing Applications, 2002, 6(3):203-205.
[18] Zou Y, Chakrabarty K. Sensor deployment and target localization based on virtual forces[J]. ACM Transactions on Embedded Computing Systems, 2004, 3(1):61-91.
[19]汪学清,杨永田.一种基于虚拟菱形网格的传感器节点布置算法[J].计算机应用, 2006, 26(7):1554-1556.
[20] Johanson P, Larsson T, Hedman N, et al. Scenario-based performance analysis of routing protocols for mobile ad-hoc networks[C]. Proceedings of the 5th Annual International Confer- ence on Mobile Computing and Networking, August 15-19, 1999, Seattle, USA, pp.195-206.
[21] Bambos N. Toward power-sensitive network architectures in wireless communications: concepts, issues, and design aspects[J]. IEEE Personal Communications, 1998, 5(6):50-59.
[22] Heinzelman WR, Kulik J, Balakrishnan H. Adaptive protocols for information disse- mination in wireless sensor networks[C]. Proceedings of the 5th Annual International Confer- ence on Mobile Computing and Networking, August 15-19, 1999, Seattle, USA, pp.174-185.
[23] Intanagonwiwat C, Govindan R, Estrin D. Directed diffusion for wireless sensor net- working[J]. IEEE/ACM Transactions on Networking, 2003, 11(1):2-16.
[24] Heinzelman WR, Chandrakasana A, Balakrishnan H. An application-specific protocol architecture for wireless micro-sensor networks[J]. IEEE Wireless Communications, 2002, 1(4): 660-670.
[25] He T, Stankovic JA, Lu CY, et al. SPEED: A stateless protocol for real-time communi- cation in sensor networks[C]. Proceedings of the 23rd International Conference on Distributed Computing Systems, May 19-22, 2003, Rhode Island, USA, pp.46-55.
[26] Raghunathan V, Schurgers C, Park S, et al. Energy-aware wireless micro-sensor networks[J]. Signal Processing Magazine, 2002, 19(2):40-50.
[27] Min R, Chadrakasan A. A framework for energy-scalable communication in high-density wireless networks[C]. Proceedings of the 2002 International Symposium on Low Power Electro- nics and Design, August 12-14, 2002, Monterey, USA, pp.36-41.
[28] Lettieri P, Schurgers C, Srivastava M. Adaptive link layer strategies for energy efficient wireless networking[J]. Wireless Networks, 1999, 5(5):339-355.
[29]陆锋.最短路径算法:分类体系与研究进展[J].测绘学报, 2001, 30(3):269-275.
[30]禹波.关于路由选择的Dijkstra算法的分析和优化[J].辽宁师专学报, 2007, 9(4):85-86.
[31]叶桥会. A*算法之启发值应用[J].福建电脑, 2008(3):103-104.
[2]牟连佳,牟连泳.无线传感网络及其在工业领域应用研究[J].工业控制计算机, 2005, 18(1):3-5.
[3]乔晓军,张馨,王成等.无线传感器网络在农业中的应用[J].农业工程学报, 2005, 21 (12):232-234.
[4]马碧春.无线传感器网络在医疗行业的应用展望[J].中国医院管理, 2006, 26(10):73.
[5]田欣,胡莲.基于无线传感网的城市应急指挥系统关键技术初探[J].经济师, 2006, (6): 53-54.
[6]饶云华,代莉,赵存成等.基于无线传感器网络的环境监测系统[J].武汉大学学报(理学版), 2006, 52(3):345-348.
[7]李光辉,赵军,王智.基于无线传感器网络的森林火灾监测预警系统[J].传感技术学报, 2006, 19(6):2761-2764.
[8]李莹莹,刘云辉,樊玮虹等.基于移动通信网络的机器人遥操作[J].通信学报, 2006, 27 (5):52-59.
[9]张志海,沈连丰,叶芝慧等.一种基于Zigbee的无线传感器网络教学实验系统[J].电气电子教学学报, 2006, 28(5):76-80.
[10]吴成东,郑君刚,刘大任等.基于无线传感器网络的智能家居网络技术研究[J].沈阳建筑大学学报, 2005, 21(6):753-756.
[11] Leonard J, Durrant-Whyte H. Mobile robot localization by tracking geometric beacons[J]. IEEE Transactions on Robotics and Automation, 1991, 7(3):376-382.
[12] Guivant J, Nebot E. Optimization of the simultaneous localization and map-building alg- orithm for real-time implementation[J]. IEEE Transactions on Robotics and Automation, 2001, 17(3):242-257.
[13] Fox D, Burgard W, Kruppa H. A probabilistic approach to collaborative multi-robot loca- lization[J]. Autonomous Robots, 2000, 8(3):325-344.
[14] Thrun S, Fox D, Burgard W, et al. Robust Monte Carlo localization for mobile robots art- ificial intelligence[J]. Artificial Intelligence, 2000, 128(1):99-141.
[15]刘丽萍,王智,孙优贤.无线传感器网络部署及其覆盖问题研究[J].电子与信息学报, 2006, 28(9):1752-1757.
[16] Akyildiz IF, Su W, Sankarasubramaniam Y, et al. Wireless sensor networks: a survey[J]. Computer Networks, 2002, 38(4):393-422.
[17] Iyengar SS, Kumar S. Preface of special issue on distributed sensor networks[J]. The International Journal of High Performance Computing Applications, 2002, 6(3):203-205.
[18] Zou Y, Chakrabarty K. Sensor deployment and target localization based on virtual forces[J]. ACM Transactions on Embedded Computing Systems, 2004, 3(1):61-91.
[19]汪学清,杨永田.一种基于虚拟菱形网格的传感器节点布置算法[J].计算机应用, 2006, 26(7):1554-1556.
[20] Johanson P, Larsson T, Hedman N, et al. Scenario-based performance analysis of routing protocols for mobile ad-hoc networks[C]. Proceedings of the 5th Annual International Confer- ence on Mobile Computing and Networking, August 15-19, 1999, Seattle, USA, pp.195-206.
[21] Bambos N. Toward power-sensitive network architectures in wireless communications: concepts, issues, and design aspects[J]. IEEE Personal Communications, 1998, 5(6):50-59.
[22] Heinzelman WR, Kulik J, Balakrishnan H. Adaptive protocols for information disse- mination in wireless sensor networks[C]. Proceedings of the 5th Annual International Confer- ence on Mobile Computing and Networking, August 15-19, 1999, Seattle, USA, pp.174-185.
[23] Intanagonwiwat C, Govindan R, Estrin D. Directed diffusion for wireless sensor net- working[J]. IEEE/ACM Transactions on Networking, 2003, 11(1):2-16.
[24] Heinzelman WR, Chandrakasana A, Balakrishnan H. An application-specific protocol architecture for wireless micro-sensor networks[J]. IEEE Wireless Communications, 2002, 1(4): 660-670.
[25] He T, Stankovic JA, Lu CY, et al. SPEED: A stateless protocol for real-time communi- cation in sensor networks[C]. Proceedings of the 23rd International Conference on Distributed Computing Systems, May 19-22, 2003, Rhode Island, USA, pp.46-55.
[26] Raghunathan V, Schurgers C, Park S, et al. Energy-aware wireless micro-sensor networks[J]. Signal Processing Magazine, 2002, 19(2):40-50.
[27] Min R, Chadrakasan A. A framework for energy-scalable communication in high-density wireless networks[C]. Proceedings of the 2002 International Symposium on Low Power Electro- nics and Design, August 12-14, 2002, Monterey, USA, pp.36-41.
[28] Lettieri P, Schurgers C, Srivastava M. Adaptive link layer strategies for energy efficient wireless networking[J]. Wireless Networks, 1999, 5(5):339-355.
[29]陆锋.最短路径算法:分类体系与研究进展[J].测绘学报, 2001, 30(3):269-275.
[30]禹波.关于路由选择的Dijkstra算法的分析和优化[J].辽宁师专学报, 2007, 9(4):85-86.
[31]叶桥会. A*算法之启发值应用[J].福建电脑, 2008(3):103-104.
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