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Geometric Spanners for Wireless Ad Hoc Networks
April 2003 (vol. 14 no. 4)
pp. 408-421

Abstract—We propose a new geometric spanner for static wireless ad hoc networks, which can be constructed efficiently in a localized manner. It integrates the connected dominating set and the local Delaunay graph to form a backbone of the wireless network. Priori arts showed that both structures can be constructed locally with bounded communication costs. This new spanner has these following attractive properties: 1) the backbone is a planar graph, 2) the node degree of the backbone is bounded from above by a positive constant, 3) it is a spanner for both hops and length, 4) it can be constructed locally and is easy to maintain when the nodes move around, and 5) moreover, the communication cost of each node is bounded by a constant. Simulation results are also presented for studying its practical performance.

[1] “IETF Mobile Ad Hoc Network Working Group,” http://www.ietf.org/html.chartersmanet-charter.html , 2002.
[2] P. Bose, P. Morin, I. Stojmenovic, and J. Urrutia, “Routing With Guaranteed Delivery in Ad Hoc Wireless Networks,” ACM/Kluwer Wireless Networks, vol. 7, no. 6, 2001.
[3] G. Calinescu, I. Mandoiu, P.J. Wan, and A. Zelikovsky, “Selecting Forwarding Neighbors in Wireless Ad Hoc Networks,” Proc. Fifth Int'l Workshop Discrete Algorithms and Methods for Mobile Computing and Comm. (DIAL M), 2001.
[4] B. Karp and H.T. Kung, “GPSR: Greedy Perimeter Stateless Routing for Wireless Networks,” Proc. Conf. Mobile Computing MOBICOM, pp. 243-254, Aug. 2000.
[5] Y.-B. Ko and N.H. Vaidya, “Using Location Information to Improve Routing in Ad Hoc Networks,” technical report, Dept. of Computer Science, Texas A&M Univ., 1997.
[6] K. Alzoubi, P.-J. Wan, and O. Frieder, “Message-Optimal Connected-Dominating-Set Construction for Routing in Mobile Ad Hoc Networks,” Proc. Third ACM Int'l Symp. Mobile Ad Hoc Networking and Computing (MobiHoc '02), 2002.
[7] B. Das and V. Bharghavan, “Routing in Ad-Hoc Networks Using Minimum Connected Dominating Sets,” Proc. 1997 IEEE Int'l Conf. Comm. (ICC '97), vol. 1, pp. 376-380, 1997.
[8] J. Wu and H. Li, “A Dominating-Set-Based Routing Scheme in Ad Hoc Wireless Networks,” The Special Issue on Wireless Networks in the Telecomm. Systems J., vol. 3, pp. 63-84, 2001.
[9] J. Wu, F. Dai, M. Gao, and I. Stojmenovic, “On Calculating Power-Aware Connected Dominating Sets for Efficient Routing in Ad Hoc Wireless Networks,” IEEE/KICS J. Comm. and Networks, vol. 4, no. 1, pp. 59-70, 2002.
[10] M. Seddigh, J. Solano Gonzalez, and I. Stojmenovic, “RNG and Internal Node Based Broadcasting Algorithms for Wireless One-to-One Networks,” ACM Mobile Computing and Comm. Rev., vol. 5, no. 2, 2001.
[11] X.-Y. Li, P.-J. Wan, Y. Wang, and O. Frieder, “Sparse Power Efficient Topology for Wireless Networks,” Proc. IEEE Hawaii Int'l Conf. System Sciences (HICSS), 2002.
[12] P. Bose, L. Devroye, W. Evans, and D. Kirkpatrick, “On the Spanning Ratio of Gabriel Graphs and Beta-Skeletons,” Proc. Latin Am. Theoretical Infocomatics (LATIN), 2002.
[13] J. Gao, L.J. Guibas, J. Hershburger, L. Zhang, and A. Zhu, “Geometric Spanner for Routing in Mobile Networks,” Proc. Second ACM Symp. Mobile Ad Hoc Networking and Computing (MobiHoc 01), 2001.
[14] J. Gao, L.J. Guibas, J. Hershburger, L. Zhang, and A. Zhu, “Discrete Mobile Centers,” Proc. 17th ACM Symp. Computational Geometry (SoCG 01), pp. 188-196, 2001.
[15] A.D. Amis, R. Prakash, T.H.P. Vuong, and D.T. Huynh, “Max-MinD-Cluster Formation in Wireless Ad Hoc Networks,” Proc. INFORCOM, pp. 32-41, 2001.
[16] R. Wattenhofer, L. Li, P. Bahl, and Y.-M. Wang, Distributed Topology Control for Power Efficient Operation in Multihop Wireless Ad Hoc Networks Proc. Infocom 2001, Apr. 2001.
[17] 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 (ICCCN01), pp. 564-567, 2001.
[18] B. Liang and Z.J. Haas, “Virtual Backbone Generation and Maintenance in Ad Hoc Network Mobility Management,” Proc. 19th Ann. Joint Conf. IEEE Computer and Comm. Soc. INFOCOM, vol. 3, pp. 1293-1302, 2000.
[19] J. Wu and H. Li, “Domination and Its Applications in Ad Hoc Wireless Networks with Unidirectional Links,” Proc. Int'l Conf. Parallel Processing 2000, pp. 189-197, 2000.
[20] K.M. Alzoubi, P.J. Wan, and O. Frieder, “New Distributed Algorithm for Connected Dominating Set in Wireless Ad Hoc Networks.” Proc. 35th Hawaii Int'l Conf. System Sciences, pp. 1-7, Jan. 2002.
[21] D.J. Baker and A. Ephremides, “The Architectureal Organization of a Mobile Radio Network via a Distributed Algorithm,” IEEE Trans. Comm., vol. 29, no. 11, pp. 1694-1701, Nov. 1981.
[22] D.J. Baker, A. Ephremides, and J.A. Flynn, The Design and Simulation of a Mobile Radio Network with Distributed Control IEEE J. Selected Areas Comm., pp. 226-237, Jan. 1984.
[23] S. Basagni, Distributed Clustering for Ad Hoc Networks Proc. Int'l Symp. Parallel Algorithms, Architectures and Networks ISPAN, pp. 310-315, June 1999.
[24] I. Chlamtac and A. Farago, “A New Approach to Design and Analysis of Peer to Peer Mobile Networks,” Wireless Networks, vol. 5, pp. 149-156, 1999.
[25] I. Stojmenovic, S. Seddigh, and J. Zunic, “Dominating Sets and Neighbor Elimination Based Broadcasting Algorithms in Wireless Networks,” IEEE Trans. Parallel and Distributed Systems, vol. 13, no. 1, pp. 14-25, Jan. 2002.
[26] M. Gerla and T.-C. Tsai, “Multicluster, Mobile, Multimedia Radio Network,” Wireless Networks, vol. 1, pp. 255–265, 1995.
[27] C.R. Lin and M. Gerla, “Adaptive Clustering in Mobile Wireless Networks,” IEEE J. Selected Areas in Communications, vol. 16, pp. 1,265–1,275, 1997.
[28] K.M. Alzoubi, “Virtual Backbone in Wireless Ad Hoc Networks,” PhD thesis, Illinois Inst. of Tech nology, 2002.
[29] X.-Y. Li, G. Calinescu, and P.-J. Wan, Distributed Construction of Planar Spanner and Routing for Ad Hoc Wireless Networks Proc. 21st Ann. Joint Conf. IEEE Computer and Comm. Socs. (INFOCOM), vol. 3, 2002.
[30] J.M. Keil and C.A. Gutwin, “The Delaunay Triangulation Closely Approximates the Complete Euclidean Graph,” Proc. First Workshop Algorithms Data Structure, 1989.
[31] J.M. Keil and C.A. Gutwin, “Classes of Graphs which Approximate the Complete Euclidean Graph,” Discr. Comp. Geom., vol. 7, pp. 13-28, 1992.
[32] J.-C. Lin, S.-N. Yang, and M.-S. Chern, “An Efficient Distributed Algorithm for Minimal Connected Dominating Set Problem,” Proc. 10th Ann. Int'l Phoenix Conf. Computers and Comm. 1991, pp. 204-210, 1991.
[33] A.D. Amis and R. Prakash, “Load-Balancing Clusters in Wireless Ad Hoc Networks,” Proc. Third IEEE Symp. Application-Specific Systems and Software Eng. Technology, 2000.
[34] Y. Wang and X.-Y. Li, Geometric Spanners for Wireless Ad Hoc Networks Proc. 22nd Int'l Conf. Distributed Computing Systems (ICDCS 2002), July 2002.
[35] S. Basagni, I. Chlamtac, and A. Farago, “A Generalized Clustering Algorithm for Peer-to-Peer Networks,” Proc. Workshop Algorithmic Aspects of Comm., 1997.
[36] J. Hightower and G. Borriello, "Location Systems for Ubiquitous Computing," Computer, vol. 34, no. 8, Aug. 2001, pp. 57-66.
[37] X.-Y. Li, “Various Intersection Graphs for Wireless Ad Hoc Networks: Simple Heuristics and PTASs,” submitted for publication, 2002.
[38] X.-Y. Li and Y. Wang, “Intersection Graphs from Wireless Ad Hoc Networks,” pending publication, 2002.
[39] X.-Y. Li and Y. Wang, “Simple Heuristics and PTASs for Intersection Graphs in Wireless Ad Hoc Networks,” ACM DialM, 2002.

Index Terms:
Connected dominating set, clustering, Delaunay triangulation, spanner, unit disk graph, localized algorithm, wireless ad hoc networks.
Citation:
Khaled Alzoubi, Xiang-Yang Li, Yu Wang, Peng-Jun Wan, Ophir Frieder, "Geometric Spanners for Wireless Ad Hoc Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 14, no. 4, pp. 408-421, April 2003, doi:10.1109/TPDS.2003.1195412
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