# Routing-efficient CDS construction in Disk-Containment Graphs

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## Abstract

In wireless networks, Connected Dominating Sets (CDSs) are widely used as virtual backbones for communications. On one hand, reducing the backbone size will reduce the maintenance overhead. So how to minimize the CDS size is a critical issue. On the other hand, when evaluating the performance of a wireless network, the hop distance between two communication nodes, which reflect the energy consumption and response delay, is of great importance. Hence how to minimize the routing cost is also a key problem for constructing the network virtual backbone. In this paper, we study the problem of constructing applicable CDS in wireless networks in terms of size and routing cost. We formulate a wireless network as a Disk-Containment Graph (DCG), which is a generalization of the Unit-Disk Graph (UDG), and we develop an efficient algorithm to construct CDS in such kind of graphs. The algorithm contains two parts and is flexible to balance the performance between the two metrics. We also analyze the algorithm theoretically. It is shown that our algorithm has provable performance in minimizing the CDS size and reducing the communication distance for routing.

## Keywords

Wireless network CDS Routing efficiency Approximation algorithm## Notes

### Acknowledgments

This research work is supported in part by National Science Foundation of USA under grants CNS 0831579 and CCF 0728851. It is also jointly sponsored by MEST, Korea under WCU (R33-2008-000-10044-0), MEST, Korea under Basic Science Research Program (2011-0012216), and MKE, Korea under ITRC NIPA-2011-(C1090-1121-0008). The research of Panos M. Pardalos and Eugene Maslov is partially supported by LATNA Laboratory, NRU HSE, RF government grant, ag. 11.G34.31.0057.

## References

- 1.Garey, M.R., Johnson, D.S.: Computers and intractability. Freeman, A Guide to the Theory of NP-Completeness, New York (1979)Google Scholar
- 2.Clark, B., Colbourn, C., Johnson, D.: Unit disk graphs. Disc. Math.
**86**, 165–177 (1990)CrossRefzbMATHMathSciNetGoogle Scholar - 3.Feige, U.: A threshold of \(\ln n\) for approximating set-cover. Proceedings of the 28th ACM Symposium on Theory of Computing, New york. pp. 314–318 (1996)Google Scholar
- 4.Guha, S., Khuller, S.: Approximation algorithms for connected dominating sets. Algorithmica
**20**, 374–387 (1998)CrossRefzbMATHMathSciNetGoogle Scholar - 5.Haynes, T.W., Hedetniemi, S.T., Slater, P.J.: Fundamentals of domination in graphs. Marcel Dekker Inc., New York (1998)zbMATHGoogle Scholar
- 6.Wan, P., Alzoubi, K., Frieder, O.: Distributed construction of connected dominating set in wireless ad hoc networks. Proceedings of the 21th Annual Joint Conference of IEEE Communication and Computer Society, pp. 1597–1604 (2002)Google Scholar
- 7.Cheng, X., Huang, X., Li, D., Wu, W., Du, D.Z.: Polynomial-time approximation scheme for minimum connected dominating set in ad hoc wireless networks. Networks
**42**(4), 202–208 (2003)CrossRefzbMATHMathSciNetGoogle Scholar - 8.Bao, L., Garcia-Luna-Aceves, J.J.: Topology management in ad hoc networks. Proceedings of the 4th ACM international symposium on Mobile ad hoc networking& computing, pp. 129–140 (2003)Google Scholar
- 9.Mohammed, K., Gewali, L., Muthukumar, V.: Generating quality dominating sets for sensor network. Proceedings of the 6th International Conference on Computational Intelligence and Multimedia Applications, pp. 204–211 (2005)Google Scholar
- 10.Dai, F., Wu, J.: On constructing k-connected k-dominating set in wireless network. J. Parallel Distrib. Comput.
**66**(7), 946–958 (2005)Google Scholar - 11.Wu, W., Du, H., Jia, X., Li, Y., Huang, S.C.H.: Minimum connected dominating sets and maximal independent sets in unit disk graphs. Theor. Comput. Sci.
**352**(1–3), 1–7 (2006)CrossRefzbMATHMathSciNetGoogle Scholar - 12.Wu, Y., Wang, F., Thai, M.T., Li, Y.: Constructing k-connected m-dominating sets in wireless sensor networks. Proceedings of Military Communications Conference, pp. 1–7 (2007)Google Scholar
- 13.Thai, M., Zhang, N., Tiwari, R., Xu, X.: On approximation algorithms of k-connected m-dominating sets in disk graphs. Theor. Comput. Sci.
**358**(1–3), 49–59 (2007)CrossRefMathSciNetGoogle Scholar - 14.Thai, M., Wang, F., Liu, D., Zhu, S., Du, D.Z.: Connected dominating sets in wireless networks with different transmission ranges. IEEE Trans. Mobile Comput.
**6**(7), 721–730 (2007)CrossRefGoogle Scholar - 15.Xing, K., Cheng, W., Park, E.K., Rotenstreich, S.: Distributed connected dominating set construction in geometric k-disk graphs. Proceedings of the 28th IEEE International Conference on Distributed, Computing Systems, pp. 673–680 (2008)Google Scholar
- 16.Wang, F., Thai, M.T., Du, D.Z.: 2-Connected virtual backbone in wireless network. IEEE Trans. Wirel. Commun.
**8**(3), 1230–1237 (2009)CrossRefGoogle Scholar - 17.Kim, D., Wu, Y., Li, Y., Zou, F., Du, D.Z.: Constructing minimum connected dominating sets with bounded diameters in wireless networks. IEEE Trans. Parallel Distrib. Systems
**20**(2), 147–157 (2009)CrossRefGoogle Scholar - 18.Kim, D., Zhang, Z., Li, X., Wang, W., Wu, W., Du, D.Z.: A better approximation algorithm for computing connected dominating sets in unit ball graphs. IEEE Trans. Mobile Comput.
**9**(8), 1108–1118 (2010)Google Scholar - 19.Kim, D., Wang, W., Li, X., Zhang, Z., Wu, W.: A new constant factor approximation for computing 3-connected m-dominating sets in homogeneous wireless networks. Proceedings of the 29th Annual Joint Conference of IEEE Communication and Computer Society, pp. 2739–2747 (2010)Google Scholar
- 20.Wang, L., Wan, P., Yao, F.F.: Minimum CDS in multihop wireless networks with disparate communication ranges. Proceedings of the 5th International Conference on Wireless algorithms, Systems, and Applications, pp. 47–56 (2010)Google Scholar
- 21.Ding, L., Wu, W., Willson, J., Du, H., Lee, W., Du, D.Z.: Efficient algorithms for topology control problem with routing cost constraints in wireless networks. IEEE Trans. Parallel Distrib. Systems
**22**(10), 1601–1609 (2011)CrossRefGoogle Scholar - 22.Du, H., Ye, Q., Wu, W., Lee, W., Li, D., Du, D.Z., Howard, S.: Constant approximation for virtual backbone construction with guaranteed routing cost in wireleess sensor netowrks. Proceedings of 30th Annual Joint Conference of IEEE Communication and Computer Society, pp. 1737–1744 (2011)Google Scholar
- 23.Ding, L., Wu, W., Willson, J.K., Wu, L., Lu, Z., Lee, W.: Constant-approximation for target coverage problem in wireless sensor networks. Proceedings of 31th Annual Joint Conference of IEEE Communication and Computer Society, pp. 1584–1592 (2012)Google Scholar
- 24.Du, H., Wu, W., Ye, Q., Li, W.D., Xu, X.: CDS-based virtual backbone construction with guaranteed routing cost in wireless sensor networks. IEEE Trans. Parallel Distrib. SystemsGoogle Scholar