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Issue No.02 - February (2009 vol.20)
pp: 147-157
Donghyun Kim , University of Texas at Dallas, Richardson
Yiwei Wu , Georgia State University, Atlanta
Yingshu Li , Georgia State University, Atlanta
Feng Zou , University of Texas at Dallas, Richardson
Ding-Zhu Du , University of Texas at Dallas, Richardson
ABSTRACT
Connected Dominating Sets (CDSs) can serve as virtual backbones for wireless networks. A smaller virtual backbone incurs less maintenance overhead. Unfortunately, computing a minimum size CDS is NP-hard, and thus most researchers in this area concentrate on how to construct smaller CDSs. However, people neglected other important metrics of network, such as diameter and average hop distances between two communication parties. In this paper, we investigate the problem of constructing quality CDS in terms of size, diameter, and Average Backbone Path Length (ABPL). We present two centralized algorithms having constant performance ratios for its size and diameter of the constructed CDS. Especially, the size of CDS computed by the second algorithm is no more than 6.906 times of its optimal solution. Furthermore, we give its distributed version, which not only can be implemented in real situation easily but also considers energy to extend network lifetime. In our simulation, we show that in average the distributed algorithm not only generates a CDS with smaller diameter and ABPL than related work but also suppresses its size well. We also show that it is more energy efficient than others in prolonging network lifetime.
INDEX TERMS
Wireless networks, connected dominating sets, distributed algorithms, energy efficiency.
CITATION
Donghyun Kim, Yiwei Wu, Yingshu Li, Feng Zou, Ding-Zhu Du, "Constructing Minimum Connected Dominating Sets with Bounded Diameters in Wireless Networks", IEEE Transactions on Parallel & Distributed Systems, vol.20, no. 2, pp. 147-157, February 2009, doi:10.1109/TPDS.2008.74
REFERENCES
 [1] I.F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, “A Survey on Sensor Networks,” IEEE Comm. Magazine, vol. 40, pp. 102-114, Aug. 2002. [2] C.R. Dow, P.J. Lin, S.C. Chen, J.H. Lin, and S.F. Hwang, “A Study of Recent Research Trends and Experimental Guidelines in Mobile Ad Hoc Networks,” Proc. 19th Int'l Conf. Advanced Information Networking and Applications (AINA'05), pp. 72-77, Mar. 2005. [3] 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. [4] S. Ni, Y. Tseng, Y. Chen, and J. Sheu, “The Broadcast Storm Problem in a Mobile Ad Hoc Network,” Proc. ACM MobiCom '99, pp. 152-162, Aug. 1999. [5] S. Guha and S. Khuller, “Approximation Algorithms for Connected Dominating Sets,” Algorithmica, vol. 20, pp. 374-387, Apr. 1998. [6] B. Das and V. Bharghavan, “Routing in Ad Hoc Networks Using Minimum Connected Dominating Sets,” Proc. Int'l Conf. Comm. (ICC '97), pp. 376-380, June 1997. [7] F. Dai and J. Wu, “On Constructing $k\hbox{-}{\rm Connected}\;k\hbox{-}{\rm Dominating}$ Set in Wireless Network,” Proc. 19th IEEE Int'l Parallel and Distributed Processing Symp. (IPDPS), 2005. [8] F. Wang, M.T. Thai, and D.-Z. Du, “2-Connected Virtual Backbone in Wireless Network,” accepted with revisions in IEEE Trans. Wireless Comm., 2007. [9] Y. Wu, F. Wang, M.T. Thai, and Y. Li, “Constructing $k\hbox{-}{\rm Connected}\;m\hbox{-}{\rm Dominating}$ Sets in Wireless Sensor Networks,” Proc. Military Comm. Conf. (MILCOM '07), Oct. 2007. [10] 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,” Theoretical Computer Science, vol. 358, pp. 49-59, 2007. [11] B. Das, R. Sivakumar, and V. Bharghavan, “Routing in Ad Hoc Networks Using a Spine,” Proc. Int'l Conf. Computers Comm. and Networks (ICCCN), 1997. [12] R. Sivakumar, B. Das, and V. Bharghavan, “An Improved Spine-Based Infrastructure for Routing in Ad Hoc Networks,” Proc. Third IEEE Symp. Computers and Comm. (ISCC '98), June 1998. [13] K. Mohammed, L. Gewali, and V. Muthukumar, “Generating Quality Dominating Sets for Sensor Network,” Proc. Sixth Int'l Conf. Computational Intelligence and Multimedia Applications (ICCIMA '05), pp. 204-211, Aug. 2005. [14] J. Wu, M. Gao, and I. Stojmenovic, “On Calculating Power-Aware Connected Dominating Sets for Efficient Routing in Ad Hoc Wireless Networks,” Proc. Int'l Conf. Parallel Processing (ICPP '01), pp. 346-356, Sept. 2001. [15] L. Ruan, H. Du, X. Jia, W. Wu, Y. Li, and K.-I. Ko, “A Greedy Approximation for Minimum Connected Dominating Sets,” J.Theoretical Computer Science, vol. 329, pp. 325-330, Dec. 2004. [16] M. Cardei, X. Cheng, X. Cheng, and D.-Z. Du, “Connected Domination in Multihop Ad Hoc Wireless Networks,” Proc. Sixth Int'l Conf. Computer Science and Informatics (CS&I '02), Mar. 2002. [17] S. Funke, A. Kesselman, U. Meyer, and M. Segal, “A Simple Improved Distributed Algorithm for Minimum CDS in Unit Disk Graphs,” ACM Trans. Sensor Network, vol. 2, no. 3, pp. 444-453, Aug. 2006. [18] J. Wu, B. Wu, and I. Stojmenovic, “Power-Aware Broadcasting and Activity Scheduling in Ad Hoc Wireless Networks Using Connected Dominating Sets,” Wireless Comm. and Mobile Computing, vol. 3, no. 2, pp. 425-438, Mar. 2003. [19] Y. Zeng, X. Jia, and Y. He, “Energy Efficient Distributed Connected Dominating Sets Construction in Wireless Sensor Networks,” Proc. Int'l Wireless Comm. and Mobile Computing Conf. (IWCMC '06), pp. 797-802, July 2006. [20] P.-J. Wan, K.M. Alzoubi, and O. Frieder, “Distributed Construction of Connected Dominating Set in Wireless Ad Hoc Networks,” Proc. IEEE INFOCOM '02, June 2002. [21] 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 (HICSS '02), p. 297, 2002. [22] K.M. Alzoubi, P.-J. Wan, and O. Frieder, “Distributed Heuristics for Connected Dominating Sets in Wireless Ad Hoc Networks,” J.Comm. and Networks, vol. 4, no. 1, Mar. 2002. [23] J. Wu and H. Li, “On Calculating Connected Dominating Set for Efficient Routing in Ad Hoc Wireless Networks,” Proc. Third ACM Int'l Workshop Discrete Algorithms and Methods for Mobile Computing and Comm. (DIALM '99), pp. 7-14, 1999. [24] 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. [25] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, 1978. [26] D.S. Johnson, “Approximation Algorithms for Combinatorial Problems,” J. Computer System Science, vol. 9, pp. 256-278, 1974. [27] B.N. Clark, C.J. Colbourn, and D.S. Johnson, “Unit Disk Graphs,” Discrete Math., vol. 86, pp. 165-177, Dec. 1990. [28] S.C.H. Huang, P.-J. Wan, C.T. Vu, Y. Li, and F. Yao, “Nearly Constant Approximation for Data Aggregation Scheduling in Wireless Sensor Networks,” Proc. IEEE INFOCOM '07, pp.366-372, May 2007. [29] S. Yang, J. Wu, and F. Dai, “Efficient Backbone Construction Methods in MANETs Using Directional Antennas,” Proc. 27th Int'l Conf. Distributed Computing Systems (ICDCS), 2007. [30] B. Awerbuch and R.G. Gallager, “A New Distributed Algorithm to Find Breadth First Search Trees,” IEEE Trans. Information Theory, vol. 33, no. 3, pp. 315-322, 1987. [31] W. Heinzelman, “Application-Specific Protocol Architectures for Wireless Networks,” PhD thesis, MIT, 2000.