Localized Delaunay Triangulation with Application in Ad Hoc Wireless Networks

IEEE Transactions on Parallel and Distributed Systems

Volumn 14, Issue 10, 2003, Pages 1035-1047

  Li, Xiang Yang ^a   Calinescu, Gruia ^a   Wan, Peng Jun ^a   Wang, Yu ^a  

^a Illinois Institute of Technology   (United States)

Author keywords

Delaunay triangulation; Localized method; Planar; Routing; Spanner; Topology control; Wireless networks

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; DISTRIBUTED COMPUTER SYSTEMS; GRAPH THEORY; MATHEMATICAL MODELS; NETWORK PROTOCOLS; ROUTERS; WIRELESS TELECOMMUNICATION SYSTEMS;

AD HOC NETWORKS; MATHEMATICAL TRIANGULATION;

PACKET NETWORKS;

EID: 0242410472     PISSN: 10459219     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPDS.2003.1239871     Document Type: Article

References (41)

1. D.B. Johnson and D.A. Maltz, "Dynamic Source Routing in Ad Hoc Wireless Networks," Mobile Computing, T. Imielinski and H.F. Korth, eds., vol. 353, Kluwer Academic, 1996.
2. S. Murthy and J. Garcia-Luna-Aceves, "An Efficient Routing Protocol for Wireless Networks," ACM Mobile Networks and Applications J., Special issue on Routing in Mobile Comm. Networks, vol. 1, no. 2, 1996.
3. V. Park and M. Corson, "A Highly Adaptive Distributed Routing Algorithm for Mobile Wireless Networks," Proc. IEEE Infocom, 1997.
4. C. Perkins, "Ad-Hoc On-Demand Distance Vector Routing," Proc. MILCOM, Nov. 1997.
5. C. Perkins and P. Bhagwat, "Highly Dynamic Destination-Sequenced Distance-Vector Routing," Proc. ACM SIGCOMM, Oct. 1994.
6. P. Sinha, R. Sivakumar, and V. Bharghavan, "CEDAR: Core Extraction Distributed Ad Hoc Routing Algorithm," IEEE J. Selected Areas in Comm., vol. 17, no. 8, pp. 1454-1465, Aug. 1999.
7. E. Royer and C. Toh, "A Review of Current Routing Protocols for Ad-Hoc Mobile Wireless Networks," IEEE Personal Comm., Apr. 1999.
8. S. Ramanathan and M. Steenstrup, "A Survey of Routing Techniques for Mobile Communication Networks," ACM/Baltzer Mobile Networks and Applications, pp. 89-104, 1996.
9. P. Bose and P. Morin, "Online Routing in Triangulations," Proc. 10th Ann. Int'l Symp. Algorithms and Computation, 1999.
10. I. Stojmenovic and X. Lin, "Loop-Free Hybrid Single-Path/Flooding Routing Algorithms with Guaranteed Delivery for Wireless Networks," IEEE Trans. Parallel and Distributed Systems, vol. 12, no. 10, 2001.
11. 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, pp. 609-616, 2001, Proc. Third Int'l Workshop Discrete Algorithms and Methods for Mobile Computing and Comm., pp. 48-55, 1999.
12. 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, pp. 609-616, 2001, Proc. Third Int'l Workshop Discrete Algorithms and Methods for Mobile Computing and Comm., pp. 48-55, 1999.
13. B. Karp and H.T. Kung, "GPSR: Greedy Perimeter Stateless Routing for Wireless Networks," Proc. ACM/IEEE Int'l Conf. Mobile Computing and Networking, 2000.
14. L. Barrire, P. Fraigniaud, and L. Narayanan, "Robust Position-Based Routing in Wireless Ad Hoc Networks with Unstable Transmission Ranges," Proc. Fifth Int'l Workshop Discrete Algorithms and Methods for Mobile Computing and Comm., pp. 19-27, 2001.
15. P. Bose, L. Devroye, W. Evans, and D. Kirkpatrick, "On the Spanning Ratio of Gabriel Graphs and Beta-Skeletons," Proc. Latin Am. Theoretical Informatics Conf., 2002.
16. D. Eppstein, "Beta-Skeletons Have Unbounded Dilation," Technical Report ICS-TR-96-15, Univ. of California, Irvine, 1996.
17. X.-Y. Li, G. Calinescu, and P.-J. Wan, "Distributed Construction of Planar Spanner and Routing for Ad Hoc Wireless Networks," Proc. 21st IEEE INFOCOM, vol. 3, 2002.
18. 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, 2001.
19. L. Hu, "Topology Control for Multihop Packet Radio Networks," IEEE Trans. Comm., vol. 41, 1993.
20. X.-Y. Li, I. Stojmenovic, and Y. Wang, "Partial Delaunay Triangulation and Degree Limited Localized Bluetooth Multihop Scatternet Formation," IEEE Trans. Parallel and Distributed Systems, 2003.
21. E. Kranakis, H. Singh, and J. Urrutia, "Compass Routing on Geometric Networks," Proc. 11th Canadian Conf. Computational Geometry, pp. 51-54, 1999.
22. 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.
23. J.M. Keil and C.A. Gutwin, "Classes of Graphs which Approximate the Complete Euclidean Graph," Discrete Compuational Geometry, vol. 7, pp. 13-28, 1992.
24. F.P. Preparata and M.I. Shamos, Computational Geometry: An Introduction. Springer-Verlag, 1985.
25. D.P. Dobkin, S.J. Friedman, and K.J. Supowit, "Delaunay Graphs are Almost as Good as Complete Graphs," Discrete Computational Geometry, pp. 399-407, 1990.
26. J.M. Keil and C.A. Gutwin, "The Delaunay Triangulation Closely Approximates the Complete Euclidean Graph," Proc. First Workshop Algorithms Data Structure, 1989.
27. P.L. Chew, "There is a Planar Graph as Good as the Complete Graph," Proc. Second Symp. Computational Geometry, pp. 169-177, 1986.
28. X.-Y. Li, P.-J. Wan, Y. Wang, and O.'Frieder, "Sparse Power Efficient Topology for Wireless Networks," J. Parallel and Distributed Computing, 2002.
29. K.R. Gabriel and.R.R. Sokal, "A New Statistical Approach to Geographic Variation Analysis," Systematic Zoology, vol. 18, pp. 259-278, 1969.
30. J. Katajainen, "The Region Approach for Computing Relative Neighborhood Graphs in the lp Metric," Computing, vol. 40, pp. 147-161, 1988.
31. G.T. Toussaint, "The Relative Neighborhood Graph of a Finite Planar Set," Pattern Recognition, vol. 12, no. 4, pp. 261-268, 1980.
32. W.Z. Wang, X.-Y. Li, K. Moaveninejad, Y. Wang, and W.-Z. Song, "The Spanning Ratios of β-Skeletons," Proc. Canadian Conf. Computational Geometry, 2003.
33. T. Lukovszki, "New Results on Geometric Spanners and Their Applications," PhD thesis, Univ. of Paderborn, 1999.
34. M. Fischer, T. Lukovszki, and M. Ziegler, "Partitioned Neighborhood Spanners of Minimal Outdegree," technical report, Heinz Nixdore Inst., Germany, 1999.
35. P. Bose, A. Brodnik, S Carlsson, E.D. Demaine, R. Fleischer, A. Lopez-Ortiz, P. Morin, and J.I. Munro, "Online Routing in Convex Subdivisions," Proc. Int'l Symp, Algorithms and Computation, pp. 47-59, 2000.
36. G. Calinescu, "Computing 2-Hop Neighborhoods in Ad Hoc Wireless Networks." 2002.
37. X.-Y. Li, P.-J. Wan, and O. Frieder, "Coverage in Wireless Ad-Hoc Sensor Networks," IEEE Trans. Computers, vol. 52, no. 6, pp. 753-763, 2003.
38. X.-Y. Li, Y. Wang, and O. Frieder, "Efficient Localized Routing for Wireless Ad Hoc Networks," Proc. IEEE Int'l Conf. Comm., 2003.
39. S. Datta, I. Stojmenovic, and J. Wu, "Internal Node and Shortcut Based Routing with Guaranteed Delivery in Wireless Networks," Proc. IEEE Int'l Conf. Distributed Computing and Systems, pp. 461-466, 2001.
40. X.-Y. Li and Y. Wang, "Efficient Construction of Low Weight Bounded Degree Spanner," Proc. Int'l Computing and Combinatorics Conf., 2003.
41. Y. Wang and X.-Y. Li, "Localized Construction of Bounded Degree and Planar Spanner for Wireless Ad Hoc Networks," submitted for publication, 2003.