Abstract
Connected dominating set is widely used in wireless ad-hoc and sensor networks as a routing and topology control backbone to improve the performance and increase the lifetime of the network. Most of the distributed algorithms for approximating connected dominating set are based on constructing maximal independent set. The performance of such algorithms highly depends on the relation between the size of the maximum independent set (mis(G)) and the size of the minimum connected dominating set (cds(G)) in the graph G. In this paper, after observing the properties of such subgraphs, we decrease the previous ratio of 3.453 to 3.0 by showing that mis(G) ≤ 3·mcds(G) + 3. Additionally, we prove that this bound is tight and cannot be improved. Finally, we present practical analysis of constructing connected dominating set based on maximal independent set in wireless networks. It is shown that the theoretical bound for unit disk graph is still practically applicable for general wireless networks.
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References
Alzoubi, K.M., Wan, P.-J., Frieder, O.: Message-optimal connected dominating sets in mobile ad hoc networks. In: MobiHoc 2002: Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing, pp. 157–164. ACM, New York (2002)
Clark, C.C.B., Johnson, D.: Unit disk graphs. Descrete Mathmatics 86, 165–177 (1990)
Das, R.S.B., Bharghavan, V.: Routing in ad-hoc networks using a virtual backbone. In: ICCCN 1997, pp. 1–20 (1997)
Banik, S.M., Radhakrishnan, S.: Minimizing broadcast latency in ad hoc wireless networks. In: ACM-SE 45: Proceedings of the 45th annual southeast regional conference, pp. 533–534. ACM, New York (2007)
Bevan Das, R.S., Bharghavan, V.: Routing in ad-hoc networks using a spine. In: Internatioal Conference on Computers and Communaation Networks, pp. 376–380 (1997)
Cardei, M., Cheng, X., Cheng, X., Du., D.-Z.: Connected domination in multihop ad hoc wireless networks. In: Proceedings of Sixth International Conference in Computer Science and Informatics, CSI
Das, B., Bharghavan, V.: Routing in ad-hoc networks using minimum connected dominating sets. In: ICC, pp. 376–380 (1997)
De Gaudenzi, T.G.F.L.M., Garde, R.: Ds-CDMA techniques for mobile and personal satellite communications: An overview. In: IEEE Second Symposium Conommunications and Vehicular Technology (1994)
Deb, B., Nath, B.: On the node-scheduling approach to topology control in ad hoc networks. In: MobiHoc 2005: Proceedings of the 6th ACM international symposium on Mobile ad hoc networking and computing, pp. 14–26. ACM, New York (2005)
Funke, S., Kesselman, A., Meyer, U., Segal, M.: A simple improved distributed algorithm for minimum CDS in unit disk graphs. ACM Transaction on Sensor Networks 2(3), 444–453 (2006)
Guha, S., Khuller, S.: Approximation algorithms for connected dominating sets. Algorithmica 20(4), 374–387 (1998)
Blum, A.T.J., Ding, M., Cheng, X.: Connected dominating set in sensor networs and manets. In: Du, D.-Z., Pardalos, P. (eds.) Handbook of Combinatorial Optimization, pp. 329–369. Kluwer Academic Publishers, Dordrecht (2004)
Marathe, M.V., Breu, H., Hunt III, H.B., Ravi, S.S., Rosenkrantz, D.J.: Simple heuristics for unit disk graphs. Networks 25, 59–68 (1995)
Min, M., Du, H., Jia, X., Huang, C.X., Huang, S.C.-H., Wu, W.: Improving construction for connected dominating set with steiner tree in wireless sensor networks. J. of Global Optimization 35(1), 111–119 (2006)
Mnif, K., Rong, B., Kadoch, M.: Virtual backbone based on mcds for topology control in wireless ad hoc networks. In: PE-WASUN 2005: Proceedings of the 2nd ACM international workshop on Performance evaluation of wireless ad hoc, sensor, and ubiquitous networks, pp. 230–233. ACM, New York (2005)
Ni, S.-Y., Tseng, Y.-C., Chen, Y.-S., Sheu, J.-P.: The broadcast storm problem in a mobile ad hoc network. In: MobiCom 1999: Proceedings of the 5th annual ACM/IEEE international conference on Mobile computing and networking, pp. 151–162. ACM, New York (1999)
Shaikh, J.A., Solano, J., Stojmenovic, I., Wu, J.: New metrics for dominating set based energy efficient activity scheduling in ad hoc networks. In: LCN 2003: Proceedings of the 28th Annual IEEE International Conference on Local Computer Networks, Washington, DC, USA, p. 726. IEEE Computer Society Press, Los Alamitos (2003)
Stojmenovic, I., Seddigh, M., Zunic, J.: Dominating sets and neighbor elimination-based broadcasting algorithms in wireless networks. IEEE Transactions on Parallel and Distributed Systems 13(1), 14–25 (2002)
Wan, P., Alzoubi, K., Frieder, O.: Distributed construction of connected dominating set in wireless ad hoc networks (2002)
Wu, J., Li, H.: On calculating connected dominating set for efficient routing in ad hoc wireless networks. In: DIALM 1999: Proceedings of the 3rd international workshop on Discrete algorithms and methods for mobile computing and communications, pp. 7–14. ACM, New York (1999)
Wu, W., Du, H., Jia, X., Li, Y., Huang, S.C.-H.: Minimum connected dominating sets and maximal independent sets in unit disk graphs. Theoretical Computer Science 352(1), 1–7 (2006)
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Vahdatpour, A., Dabiri, F., Moazeni, M., Sarrafzadeh, M. (2008). Theoretical Bound and Practical Analysis of Connected Dominating Set in Ad Hoc and Sensor Networks. In: Taubenfeld, G. (eds) Distributed Computing. DISC 2008. Lecture Notes in Computer Science, vol 5218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87779-0_33
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DOI: https://doi.org/10.1007/978-3-540-87779-0_33
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