Subscribe
Issue No.05 - May (2013 vol.12)
pp: 909-916
Lixin Wang , Dept. of Math., Paine Coll., Augusta, GA, USA
Peng-Jun Wan , Dept. of Comput. Sci., Illinois Inst. of Technol., Chicago, IL, USA
Frances Yao , Inst. for Theor. Comput. Sci., Tsinghua Univ., Beijing, Chile
ABSTRACT
Connected dominating set (CDS) has a wide range of applications in multihop wireless networks. The Minimum CDS problem has been studied extensively in multihop wireless networks with uniform communication ranges. However, in practice, the nodes may have different communication ranges either because of the heterogeneity of the nodes, or due to interference mitigation, or due to a chosen range assignment for energy conservation. In this paper, we present a greedy approximation algorithm for computing a Minimum CDS in multihop wireless networks with disparate communications ranges and prove that its approximation ratio is better than the best one known in the literature. Our analysis utilizes a tighter relation between the independence number and the connected domination number.
INDEX TERMS
Wireless networks, Approximation methods, Spread spectrum communication, Approximation algorithms, Upper bound, Mobile computing, Electronic mail, virtual backbone, Connected dominating set, independent set, disk graph, wireless network
CITATION
Lixin Wang, Peng-Jun Wan, Frances Yao, "Minimum CDS in Multihop Wireless Networks with Disparate Communication Ranges", IEEE Transactions on Mobile Computing, vol.12, no. 5, pp. 909-916, May 2013, doi:10.1109/TMC.2012.58
REFERENCES
 [1] K.M. Alzoubi, P.-J. Wan, and O. Frieder, “Message-Optimal Connected Dominating Sets in Mobile Ad Hoc Networks,” Proc. ACM MobiHoc, 2002. [2] 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, 2004. [3] B.N. Clark, C.J. Colbourn, and D.S. Johnson, “Unit Disk Graphs,” Discrete Math., vol. 86, pp. 165-177, 1990. [4] F. Fodor, “The Densest Packing of 13 Congruent Circles in a Circle,” Beitrage Algebra Geometry, vol. 44, no. 2, pp. 431-440, 2003. [5] Y.S. Li, M.T. Thai, F. Wang, C.-W. Yi, P.-J. Wan, and D.-Z. Du, “On Greedy Construction of Connected Dominating Sets in Wireless Networks,” Wiley J. Wireless Comm. and Mobile Computing, vol. 5, no. 8, pp. 927-932, 2005. [6] M.T. Thai, F. Wang, D. Liu, S. Zhu, and D.-Z. Du, “Connected Dominating Sets in Wireless Networks with Different Communication Ranges,” IEEE Trans. Mobile Computing, vol. 6, no. 7, pp. 721-730, July 2007. [7] P.-J. Wan, K.M. Alzoubi, and O. Frieder, “Distributed Construction of Connected Dominating Set in Wireless Ad Hoc Networks,” ACM/Springer Mobile Networks and Applications, vol. 9, no. 2, pp. 141-149, 2004. [8] P.-J. Wan, L. Wang, and F. Yao, “Two-Phased Approximation Algorithms for Minimum CDS in Wireless Ad Hoc Networks,” Proc. IEEE Int'l Conf. Distributed Computing Systems (ICDCS '08), pp. 337-344, 2008. [9] K. Xing, W. Cheng, E.K. Park, and S. Rotenstreich, “Distributed Connected Dominating Set Construction in Geometric $k$ -Disk Graphs,” IEEE IEEE Int'l Conf. Distributed Computing Systems (ICDCS '08), pp. 673-680, 2008.