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A PTAS for minimum d-hop connected dominating set in growth-bounded graphs

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Abstract

In this paper, we design the first polynomial time approximation scheme for d-hop connected dominating set (d-CDS) problem in growth-bounded graphs, which is a general type of graphs including unit disk graph, unit ball graph, etc. Such graphs can represent majority types of existing wireless networks. Our algorithm does not need geometric representation (e.g., specifying the positions of each node in the plane) beforehand. The main strategy is clustering partition. We select the d-CDS for each subset separately, union them together, and then connect the induced graph of this set. We also provide detailed performance and complexity analysis.

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References

  1. Chen, G., Nocetti, F., Gonzalez, J., Stojmenovic, I.: Connectivity based k-hop clustering in wireless networks. In: Proceedings of the 35th Hawaii International Conference on System Sciences (2002)

  2. Cheng X., Huang X., Li D., Du D.: Polynomial-time approximation scheme for minimum CDS in ad hoc wireless networks. Networks 42, 202–208 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cheng X., Ding M., Du H., Jia X.: Virtual backbone construction in multihop ad hoc wireless networks. Wireless Commun. Mobile Comput. 6, 183–190 (2006)

    Article  Google Scholar 

  4. Cokuslu, D., Erciyes, K.: A hierarchical connected dominating set based clustering algorithm for mobile ad hoc networks. In: Proceedings of 15th Annual Meeting of the IEEE International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS2007, IEEE), pp. 61–66, October 24–26, Istanbul (2007)

  5. Gao, X., Li, X., Wu, W.: A Constant-factor approximation for d-hop connected dominating sets in unit disk graphs. IEEE Trans. Mobile Comput. (2008, submitted)

  6. Gfeller, B.,Vicari, E.: A faster distributed approximation scheme for the connected dominating set problems for growth-bounded graphs. In: Proceedings of the 6th Ad-Hoc, Mobile, and Wireless Networks International Conference (ADHOC-NOW 2007). LNCS 4686, pp. 59–73. Springer, Berlin (2007)

  7. Nguyen, T., Huynh, D.: Connected D-hop dominating sets in mobile ad hoc networks. In: Proceedings of Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, 1–8 April (2006)

  8. Nieberg, T., Hurink, J.: A PTAS for the minimum dominating set problem in unit disk graphs. Third Workshop on Approximation and Online Algorithms: part of ALGO 2005 (WAOA 2005). LNCS 3879, pp. 296–306, Springer, Berlin (2006)

  9. Nocetti, F., Gonzalez, J., Stojmenovic, I.: Connectivity based k-hop clustering in wireless networks. Telecommunication Syst. 22, 1–4, 205–220 (2003)

    Google Scholar 

  10. Rieck M., Pai S., Dhar S.: Distributed routing algorithms for multi-hop ad hoc networks using d-hop connected d-dominating sets. Comput. Netw. 47(6), 785–799 (2005)

    Article  MATH  Google Scholar 

  11. Shi, Z., Srimani, P.: A new adaptive distributed routing protocol using d-hop dominating sets for mobile ad hoc networks. In: Proceedings of the 2004 International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA’04), Las Vegas, June 21–24 (2004)

  12. Spohn, M., Garcia-Luna-Aceves, J.: Enhancing broadcast operations in ad hoc networks with two-hop connected dominating sets. In: Proceedings of the 1st IEEE International Conference on Mobile Ad-hoc and Sensor Systems (MASS’04), October 24–27, Fort Lauderdale, Florida, USA (2004)

  13. Vuong, T., Huynh, D.: Adapting d-hop dominating sets to topology changes in ad hoc networks. In: Proceedings Ninth International Conference on Computer Communications and Networks, pp. 348–353 (2000)

  14. Yau S., Gao W.: Multi-hop clustering based on neighborhood benchmark in mobile ad-hoc networks. Mobile Netw. Appl. 12(5–6), 381–391 (2007)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, Richardson, USA

    Xiaofeng Gao & Weili Wu

  2. School of Science, Xi’an Jiaotong University, Xi’an, People’s Republic of China

    Wei Wang

  3. College of Mathematics and System Sciences, Xinjiang University, Xinjiang, People’s Republic of China

    Zhao Zhang

  4. Department of Computer Science and Engineering, University of Minnesota, Minneapolis, USA

    Shiwei Zhu

Authors
  1. Xiaofeng Gao
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  2. Wei Wang
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  3. Zhao Zhang
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  4. Shiwei Zhu
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  5. Weili Wu
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Correspondence to Xiaofeng Gao.

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Gao, X., Wang, W., Zhang, Z. et al. A PTAS for minimum d-hop connected dominating set in growth-bounded graphs. Optim Lett 4, 321–333 (2010). https://doi.org/10.1007/s11590-009-0148-3

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  • DOI: https://doi.org/10.1007/s11590-009-0148-3

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