The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.09 - September (2008 vol.7)
pp: 1098-1109
ABSTRACT
Since there is no fixed infrastructure in wireless ad hoc networks , virtual backbone has been proposed as the routing infrastructure to alleviate the broadcasting storm problem. The virtual backbone construction has been studied extensively in {\em undirected} graphs, especially in unit disk graphs, in which each node has the same transmission range. In practice, however, transmission ranges of all nodes are not necessarily equal. In this paper, we model such a network as a disk graph, where unidirectional links are considered. To study the virtual backbone construction in disk graphs, we consider two problems: Strongly Connected Dominating Set (SCDS) and Strongly Connected Dominating and Absorbing Set (SCDAS). We propose a constant approximation algorithm and discuss its improvements for the SCDS problem . We also propose a heuristic for the SCDAS problem. Through extensive simulations, we verify our theoretical analysis and also demonstrate that the SCDS can be extended to form an SCDAS with marginal extra overhead.
INDEX TERMS
Wireless communication, Algorithm/protocol design and analysis, Combinatorial algorithms
CITATION
My T. Thai, Ravi Tiwari, Ding-Zhu Du, "On Construction of Virtual Backbone in Wireless Ad Hoc Networks with Unidirectional Links", IEEE Transactions on Mobile Computing, vol.7, no. 9, pp. 1098-1109, September 2008, doi:10.1109/TMC.2008.22
REFERENCES
[1] B. Clack, C. Colbourn, and D. Johnson, “Unit Disk Graphs,” Discrete Math., vol. 86, pp. 165-177, 1990.
[2] M.R. Garey and D.S. Johnson, Computers and Intractability. A Guide to the Theory of NP-Completeness. Freeman, New York, 1979.
[3] M. Park, C. Wang, J. Willson, M.T. Thai, W. Wu, and A. Farago, “A Dominating and Absorbent Set in Wireless Ad-Hoc Networks with Different Transmission Range,” Proc. ACM MobiHoc, 2007.
[4] Y. Li, S. Zhu, M.T. Thai, and D.-Z. Du, “Localized Construction of Connected Dominating Set in Wireless Networks,” NSF Int'l Workshop Theoretical Aspects of Wireless Ad Hoc, Sensor and Peer-to-Peer Networks (TAWN), 2004.
[5] P.-J. Wan, K.M. Alzoubi, and O. Frieder, “Distributed Construction on Connected Dominating Set in Wireless Ad Hoc Networks,” Proc. IEEE INFOCOM, 2002.
[6] Y. Li, M.T. Thai, F. Wang, C.-W. Yi, P.-J. Wang, and D.-Z. Du, “OnGreedy Construction of Connected Dominating Sets in Wireless Networks,” Wireless Comm. and Mobile Computing (WCMC), special issue, 2005.
[7] M. Cardei, M.X. Cheng, X. Cheng, and D.-Z. Du, “Connected Domination in Ad Hoc Wireless Networks,” Proc. Sixth Int'l Conf. Computer Science and Informatics (CSI), 2002.
[8] S. Guha and S. Khuller, “Approximation Algorithms for Connected Dominating Sets,” Algorithmica, vol. 20, pp. 374-387, 1998.
[9] L. Ruan, H. Du, X. Jia, W. Wu, Y. Li, and L.-I. Ko, “A Greedy Approximation for Minimum Connected Dominating Sets,” Theoretical Computer Science, vol. 329, nos. 1-3, pp. 325-330, Dec. 2004.
[10] M.T. Thai, F. Wang, D. Liu, S. Zhu, and D.Z. Du, “Connected Dominating Sets in Wireless Networks with Different Transmission Ranges,” IEEE Trans. Mobile Computing, vol. 6, no. 7, July 2007.
[11] M.T. Thai, N. Zhang, R. Tiwari, and X. Xu, “On Approximation Algorithms of $k\hbox{-}{\rm Connected}$ $m\hbox{-}{\rm Dominating\; Sets}$ in Disk Graphs,” J.Theoretical Computer Science, vol. 358, pp. 49-59, 2007.
[12] M.T. Thai and D.-Z. Du, “Connected Dominating Sets in Disk Graphs with Bidirectional Links,” IEEE Comm. Letters, vol. 10, no. 3, pp. 138-140, Mar. 2006.
[13] F. Wang, M.T. Thai, and D.Z. Du, “On the Construction of 2-Connected Virtual Backbone in Wireless Network,” IEEE Trans. Wireless Comm., accepted with revisions, 2006.
[14] X. Cheng, X. Huang, D. Li, W. Wu, and D.-Z. Du, “Polynomial-Time Approximation Scheme for Minimum Connected Dominating Set in Ad Hoc Wireless Networks,” Networks, vol. 42, no. 4, pp.202-208, 2003.
[15] X. Cheng, M. Ding, D.H. Du, and X. Jia, “Virtual Backbone Construction in Multi-hop Ad Hoc Wireless Networks,” Wireless Comm. and Mobile Computing, vol. 6, pp. 183-190, 2006.
[16] J. Blum, M. Ding, and X. Cheng, “Applications of Connected Dominating Sets in Wireless Networks,” Handbook of Combinatorial Optimization, D.-Z. Du and P. Pardalos, eds., pp. 329-369, Kluwer Academic Publisher, 2004.
[17] B. Das, R. Sivakumar, and V. Bharghavan, “Routing in Ad Hoc Networks Using a Spine,” Proc. Sixth Int'l Conf. Computer Comm. and Networks (ICCCN), 1997.
[18] J. Wu, “Extended Dominating-Set-Based Routing in Ad Hoc Wireless Networks with Unidirectional Links,” IEEE Trans. Parallel and Distributed Computing, vol. 22, nos. 1-4, pp. 327-340, 2002.
[19] F. Dai and J. Wu, “An Extended Localized Algorithms for Connected Dominating Set Formation in Ad Hoc Wireless Networks,” IEEE Trans. Parallel and Distributed Systems, vol. 15, no. 10, Oct. 2004.
[20] S.-Y. Ni, Y.-C. Tseng, Y.-S. Chen, and J.-P. Sheu, “The Broadcast Storm Problem in a Mobile Ad Hoc Network,” Proc. ACM MobiCom, 1999.
[21] P. Sinha, R. Sivakumar, and V. Bharghavan, “Enhancing Ad Hoc Routing with Dynamic Virtual Infrastructures,” Proc. IEEE INFOCOM, 2001.
[22] A. Ephremides, J. Wieselthier, and D. Baker, “A Design Concept for Reliable Mobile Radio Networks with Frequency Hopping Signaling,” Proc. IEEE, vol. 75, no. 1, pp. 56-73, 1987.
[23] S. Funke, A. Kesselman, U. Meyer, and M. Segal, “Simple Improved Distributed Algorithm for Minimum CDS in Unit Disk Graphs,” ACM Trans. Sensor Network, vol. 2, no. 3, pp. 444-454, Aug. 2006.
22 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool