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Using Local Geometry for Tunable Topology Control in Sensor Networks
February 2009 (vol. 8 no. 2)
pp. 218-230
Sameera Poduri, University of Southern California, Los Angeles
Sundeep Pattem, University of Southern California, Los Angeles
Bhaskar Krishnamachari, University of Southern California, Los Angeles
Gaurav S. Sukhatme, University of Southern California, Los Angeles
Neighbor-Every-Theta (NET) graphs are such that each node has at least one neighbor in every theta angle sector of its communication range. We show that for θ < π, NET graphs are guaranteed to have an edge-connectivity of at least floor(2π)/θ, even with an irregular communication range. Our main contribution is to show how this family of graphs can achieve tunable topology control based on a single parameter θ. Since the required condition is purely local and geometric, it allows for distributed topology control. For a static network scenario, a power control algorithm based on the NET condition is developed for obtaining k-connected topologies and shown to be significantly efficient compared to existing schemes. In controlled deployment of a mobile network, control over positions of nodes can be leveraged for constructing NET graphs with desired levels of network connectivity and sensing coverage. To establish this, we develop a potential fields based distributed controller and present simulation results for a large network of robots. Lastly, we extend NET graphs to 3D and provide an efficient algorithm to check for the NET condition at each node. This algorithm can be used for implementing generic topology control algorithms in 3D.

[1] P. Santi, Topology Control in Wireless Ad Hoc and Sensor Networks. John Wiley & Sons, 2005.
[2] X.-Y. Li, Ad Hoc Networking, chapter on Topology Control in Wireless Ad Hoc Networks, IEEE Press, 2003.
[3] X. Li, I. Stojmenovic, and Y. Wang, “Partial Delaunay Triangulation and Degree Limited Localized Bluetooth Scatternet Formation,” IEEE Trans. J. Parallel and Distributed Systems, vol. 15, no. 4, pp. 350-361, Apr. 2004.
[4] K. Chintalapudi, J. Paek, N. Kothari, S. Rangwala, J. Caffrey, R. Govindan, E. Johnson, and S. Masri, “Monitoring Civil Structures with a Wireless Sensor Network,” IEEE Internet Computing, vol. 10, no. 2, pp. 26-34, Mar.-Apr. 2006.
[5] G.S. Sukhatme, A. Dhariwal, B. Zhang, C. Oberg, B. Stauffer, and D.A. Caron, “The Design and Development of a Wireless Robotic Networked Aquatic Microbial Observing System,” Environmental Eng. Science, vol. 24, no. 2, pp. 205-215, 2006.
[6] R. Clayton, Mase: Shallow Subduction in Central Mexico, progress report, Sept. 2006.
[7] M.H. Rahimi, H. Shah, G.S. Sukhatme, J. Heidemann, and D. Estrin, “Studying the Feasibility of Energy Harvesting in a Mobile Sensor Network,” Proc. IEEE Int'l Conf. Robotics and Automation (ICRA '03), pp. 19-24, Sept. 2003.
[8] R. Pon, M. Batalin, J. Gordon, A. Kansal, D. Liu, M. Rahimi, L. Shirachi, Y. Yu, M. Hansen, W.J. Kaiser, M. Srivastava, G. Sukhatme, and D. Estrin, “Networked Infomechanical Systems: A Mobile Embedded Networked Sensor Platform,” Proc. IEEE/ACM Fourth Int'l Conf. Information Processing in Sensor Networks (IPSN '05), pp. 376-381, Apr. 2005.
[9] J. Zhao and R. Govindan, “Understanding Packet Delivery Performance in Dense Wireless Sensor Networks,” Proc. ACM Conf. Embedded Networked Sensor Systems (SenSys '03), pp. 1-13, Nov. 2003.
[10] M. Zuniga and B. Krishnamachari, “Analyzing the Transitional Region in Low Power Wireless Links,” Proc. IEEE Int'l Conf. Sensor and Ad Hoc Comm. and Networks (SECON '04), pp. 517-526, Oct. 2004.
[11] R. Wattenhofer, L. Li, P. Bahl, and Y.M. Wang, “A Cone-Based Distributed Topology-Control Algorithm for Wireless Multi-Hop Networks,” IEEE/ACM Trans. Networking, vol. 13, no. 1, pp. 147-159, Feb. 2005.
[12] X.-Y. Li, P-J. Wan, and Y. Wang, “Power Efficient and Sparse Spanner for Wireless Ad Hoc Networks,” Proc. IEEE Int'l Conf. Computer Comm. and Networks (ICCCN '01), pp. 564-567, Oct. 2001.
[13] M. Bahramgiri, M. Hajiaghayi, and V.S. Mirrokni, “Fault-Tolerant and 3-Dimensional Distributed Topology Control Algorithms in Wireless Multi-Hop Networks,” ACM/Kluwer Wireless Networks, vol. 12, no. 2, pp. 179-188, 2006.
[14] B.P. Gerkey, R.T. Vaughan, and A. Howard, “The Player/Stage Project: Tools for Multi-Robot and Distributed Sensor Systems,” Proc. Int'l Conf. Advanced Robotics (ICAR '03), pp.317-323, June 2003.
[15] S. Poduri, S. Pattem, B. Krishnamachari, and G.S. Sukhatme, “Sensor Network Configuration and the Curse of Dimensionality,” Proc. IEEE Workshop Embedded Networked Sensors (EmNets '06), May 2006.
[16] R. Diestel, Graph Theory, Graduate Texts in Mathematics, second ed., vol. 173, Springer, 2000.
[17] A. Kroller, S.P. Fekete, D. Pfisterer, and S. Fischer, “Deterministic Boundary Recognition and Topology Extraction for Large Sensor Networks,” Proc. ACM-SIAM Symp. Discrete Algorithm (SODA '06), pp. 1000-1009, 2006.
[18] F. Xue and P.R. Kumar, “The Number of Neighbors Needed for Connectivity of Wireless Networks,” Wireless Networks, vol. 10, no. 2, pp. 169-181, 2004.
[19] H-S. Na, C-N. Lee, and O. Cheong, “Voronoi Diagrams on the Sphere,” Computational Geometry Theory Applications, vol. 23, no. 2, pp. 183-194, 2002.
[20] E.H. Jennings and C.M. Okino, “Topology Control for Efficient Information Dissemination in Ad-Hoc Networks,” Proc. Int'l Symp. Performance Evaluation of Computer and Telecomm. Systems (SPECTS '02), July 2002.
[21] G. Xing, X. Wang, Y. Zhang, C. Lu, R. Pless, and C. Gill, “Integrated Coverage and Connectivity Configuration for Energy Conservation in Sensor Networks,” ACM Trans. Sensor Networks, vol. 1, no. 1, pp. 36-72, Aug. 2005.
[22] H. Zhang and J.C. Hou, “Maintaining Sensing Coverage and Connectivity in Large Sensor Networks,” Ad Hoc and Sensor Wireless Networks, vol. 1, nos. 1-2, pp. 89-123, Jan. 2005.
[23] A. Howard, M.J. Matarić, and G.S. Sukhatme, “Mobile Sensor Network Deployment Using Potential Fields: A Distributed, Scalable Solution to the Area Coverage Problem,” Proc. Int'l Symp. Distributed Autonomous Robotic Systems (DARS '02), pp. 299-308, 2002.
[24] S. Poduri and G.S. Sukhatme, “Constrained Coverage for Mobile Sensor Networks,” Proc. IEEE Int'l Conf. Robotics and Automation (ICRA '04), pp. 165-172, May 2004.
[25] M.M. Zavlanos and G.J. Pappas, “Potential Fields for Maintaining Connectivity of Mobile Networks,” IEEE Trans. Robotics, vol. 23, no. 4, pp. 812-816, 2007.
[26] A.C.-C. Yao, “On Constructing Minimum Spanning Trees in K-Dimensional Spaces and Related Problems,” SIAM J. Computing, vol. 11, pp. 721-736, 1982.
[27] R.M. D'Souza, D. Galvin, C. Moore, and D. Randall, “Global Connectivity from Local Geometric Constraints for Sensor Networks with Various Wireless Footprints,” Proc. ACM/IEEE Int'l Conf. Information Processing in Sensor Networks (IPSN '06), pp. 19-26, Apr. 2006.
[28] X.-Y. Li, P.-J. Wan, Y. Wang, and C.-W. Yi, “Fault Tolerant Deployment and Topology Control in Wireless Networks,” Proc. ACM MobiHoc '03, pp. 117-128, June 2003.
[29] I. Stojmenovic, “Dominating Set Based Bluetooth Scatternet Formation with Localized Maintenance,” Proc. IEEE Int'l Parallel and Distributed Processing Symp. (IPDPS '02), p. 122, Apr. 2002.
[30] F. Xue and P.R. Kumar, “On the Theta-Coverage and Connectivity of Large Random Networks,” IEEE Trans. Information Theory, vol. 52, no. 6, pp. 2289-2299, 2006.
[31] J. Cortes, S. Martinez, and F. Bullo, “Spatially-Distributed Coverage Optimization and Control with Limited-Range Interactions,” ESAIM: Control, Optimisation and Calculus of Variations, vol. 11, pp.691-719, 2005.
[32] A. Ghosh, Y. Wang, and B. Krishnamachari, “Efficient Distributed Topology Control in 3-Dimensional Wireless Networks,” Proc. IEEE Comm. Soc. Conf. Sensor, Mesh and Ad Hoc Comm. and Networks (SECON '07), pp. 91-100, June 2007.
[33] R. Wattenhofer and A. Zollinger, “XTC: A Practical Topology Control Algorithm for Ad-Hoc Networks,” Proc. IEEE Int'l Workshop Algorithms for Wireless, Mobile, Ad Hoc and Sensor Networks (WMAN), 2004.

Index Terms:
Distributed networks, Sensor networks, Algorithm/protocol design and analysis
Sameera Poduri, Sundeep Pattem, Bhaskar Krishnamachari, Gaurav S. Sukhatme, "Using Local Geometry for Tunable Topology Control in Sensor Networks," IEEE Transactions on Mobile Computing, vol. 8, no. 2, pp. 218-230, Feb. 2009, doi:10.1109/TMC.2008.95
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