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Wireless networking, dominating and packing

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Abstract

Recently, there are many papers published in the literature on study of dominating sets, connected dominating sets and their variations motivated from various applications in wireless networks and social networks. In this article, we survey those developments for wireless networking, dominating, and packing problems.

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References

  1. Alzoubi, K.M., Wan, P.-J., Frieder, O.: Message-optimal connected dominating sets in mobile ad hoc networks. In: Proceedings of the 3rd ACM International Symposium on Mobile Ad Hoc Networking and Computing, Lausanne, Switzerland, 9–11 June 2002

  2. Ambuehl, C., Erlebach, T., Mihalak, M., Nunkesser M.: Constant-factor approximation for minimum-weight (connected) dominating sets in unit disk graphs. In: Proceedings of the 9th Workshop on Approximation Algorithms for Combinatorial Optimization Problems, LNCS 4110, pp. 3–14. Springer (2006)

  3. Bharghavan, V., Das, B.: Routing in ad hoc networks using minimum connected dominating sets. In: International Conference on Communication, Montreal, Canada, June 1997

  4. Butenko, S., Ursulenko, O.: On minimum connected dominating set problem in unit-ball graphs. Preprint

  5. Cadei, M., Cheng, M.X., Cheng, X., Du, D.-Z.: Connected domination in ad hoc wireless networks. In: Proceedings of the Sixth International Conference on Computer Science and Informatics (CS&I’2002) (2002)

  6. Chang M.-S.: Efficient algorithms for the domination problems on interval and circular-arc graphs. SIAM J. Comput. 27, 1671–1694 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  7. Chen D., Du D.-Z., Hu X., Lin G.-H., Wang L., Xue G.: Approximations for Steiner trees with minimum number of Steiner points. J. Glob. Optim. 18, 17–33 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Chen, Y.P., Liestman, A.L.: Approximating minimum size weakly-connected dominating sets for clustering mobile ad hoc networks. In: Proceedings of the Third ACM International Symposium on Mobile Ad Hoc Networking and Computing, Lausanne, Switzerland, 9–11 June 2002

  9. Cheng X., Huang X., Li D., Wu W., Du D.-Z.: A polynomial-time approximation scheme for minimum connected dominating set in ad hoc wireless networks. Networks 42, 202–208 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. Clark B.N., Colbourn C.J., Johnson D.S.: Unit disk graphs. Discrete Math. 86, 165–177 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  11. Clark, W.E., Dunning, L.A.: Tight upper bounds for the domination numbers of graphs with given order and minimum degree. Electron. J. Comb. 4(1) (1997). Research paper R 26, 25 pp

  12. Dai D., Yu C.: A (5 + ε)-approximation algorithm for minimum weighted dominating set in unit disk graph. Theor. Comput. Sci. 410, 756–765 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  13. Du, D.-Z., Graham, R.L., Pardalos, P.M., Wan, P.-J., Wu, W., Zhao, W.: Analysis of Greedy approximations with nonsubmodular potential functions. In: Proceedings of the 19th Annual ACM-SIAM Symposium on Dicrete Algorithms (SODA), pp. 167–175, San Francisco, USA, 20–22 January 2008

  14. Du, D.-Z., Wang, L., Xu, B.: The Euclidean bottleneck Steiner tree and Steiner tree with minimum number of Steiner Points. COCOON’2001, pp. 509–518

  15. Eriksson, H.: MBone: the multicast backbone. In: Communications of the ACM. August 1994

  16. Feige, U.: A threshold of ln n for approximating set-cover. In: Proceedings of the 28th ACM Symposium on Theory of Computing, pp. 314–318 (1996)

  17. Funke S., Kesselman A., Meyer U.: A simple improved distributed algorithm for minimum CDS in unit disk graphs. ACM Trans. Sensor Netw. 2, 444–453 (2006)

    Article  Google Scholar 

  18. Funke S., Kesselman A., Kuhn F., Lotker Z., Sega M.: Improved approximation algorithms for connected sensor cover. Wireless Netw. 13, 153–164 (2007)

    Article  Google Scholar 

  19. Gao X., Wang Y., Li X., Wu W.: Analysis on theoretical bonds for approximating dominating set problems. Discrete Math. Algorithms Appl. 1(1), 71–84 (2009)

    Article  MATH  Google Scholar 

  20. Gao, X., Huang, Y., Zhang, Z., Wu, W.: (6 + ε)-Approximation for minimum weight dominating set in unit disk graphs. COCOON, pp. 551–557 (2008)

  21. Garey M.R., Johnson D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)

    MATH  Google Scholar 

  22. Guha S., Khuller S.: Approximation algorithms for connected dominating sets. Algorithmica 20, 374–387 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  23. 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. Syst. (TPDS) 20(2), 147–157 (2009)

    Article  Google Scholar 

  24. Li D., Liu L., Yang H.: Minimum connected r-hop k-dominating set in wireless networks. Discrete Math. Algorithms Appl. 1(1), 45–57 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  25. Li, M., Wan, P.-J., Yao, F.F.: Tighter approximation bounds for minimum CDS in wireless ad hoc networks. In: ISAAC’2009, pp. 677–686 (2009)

  26. Li Y.S., Thai M.T., Wang F., Yi C.-W., Wan P.-J., Du D.-Z.: On greedy construction of connected dominating sets in wireless networks. Wiley J. Wireless Commun. Mobile Comput. 5, 927–932 (2005)

    Article  Google Scholar 

  27. Lin G.-H., Xue G.L.: Steiner tree problem with minimum number of Steiner points and bounded edge-length. Inf. Process. Lett. 69, 53–57 (1999)

    Article  MathSciNet  Google Scholar 

  28. Min M., Huang X., Huang C.-H., Wu W., Du H., Jia X.: Improving construction for connected dominating set with Steiner tree in wireless sensor networks. J. Glob. Optim. 35, 111–119 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  29. Nieberg T., Hurink J., Kern W.: Approximation schemes for wireless networks. ACM Trans. Algorithms 4, 1–17 (2008)

    Article  MathSciNet  Google Scholar 

  30. Robin, G., Zelikovsky, A.: Improved Steiner trees approximation in graphs. In: SIAM-ACM Symposium on Discrete Algorithms (SODA), pp. 770–779, San Francisco, CA, January 2000

  31. Ruan L., Du H., Jia X., Wu W., Li Y., Ko K.-I.: A greedy approximation for minimum connected dominating set. Theor. Comput. Sci. 329, 325–330 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  32. Salhieh, A., Weinmann, J., Kochha, M., Schwiebert, L.: Power efficient topologies for wireless sensor networks. In: ICPP’2001, pp. 156–163

  33. Sampathkumar E., Walikar H.B.: The connected domination number of a graph. J. Math. Phys. Sci. 13, 607–613 (1979)

    MATH  MathSciNet  Google Scholar 

  34. Sivakumar, R., Das, B., Bharghavan, V.: An improved spine-based infrastructure for routing in ad hoc networks. In: IEEE Symposium on Computer and Communications, Athens, Greece, June 1998

  35. Sorokin A., Boyko N., Boginski V., Uryasev S., Pardalos P.M.: Mathematical programming techniques for sensor networks. Algorithms 2, 565–581 (2009)

    Article  Google Scholar 

  36. Stojmenovic, I., Seddigh, M., Zunic, J.: Dominating sets and neighbor elimination based broadcasting algorithms in wireless networks. In: Proceedings of IEEE Hawaii International Conference on System Sciences, January 2001

  37. Wan, P.-J., Alzoubi, K.M., Frieder, O.: Distributed construction of connected dominating set in wireless ad hoc networks. ACM/Springer Mobile Netw. Appl. 9(2), 141–149. A preliminary version of this paper appeared in IEEE INFOCOM 2002 (2004)

  38. Wan, P.-J., Wang, L., Yao, F.: Two-phased approximation algorithms for minimum CDS in wireless ad hoc networks. In: IEEE ICDCS, pp. 337–344 (2008)

  39. Wang Y., Li X.Y.: Localized construction of bounded degree and planar spanner for wireless ad hoc networks. Mobile Netw. Appl. 11(2), 161–175 (2006)

    Article  Google Scholar 

  40. Wang, Z., Wang, W., Kim, JU., Shan, S., Thuraisingham, B., Wu, W.: PTAS for minimum weighted dominating set in sparse graphs. J. Glob. Optim. (submitted)

  41. Willson, J., Gao, X., Qu, Z., Zhu,Y., Li, Y., Wu, W.: Efficient distributed algorithms for topology control problem with shortest path constraints. (submitted)

  42. Wu, J., Li, H.: On calculating connected dominating set for efficient routing in ad hoc wireless networks. In: Proceedings of the 3rd ACM International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, pp. 7–14 (1999)

  43. Wu, W., Du, H., Jia, X., Li, Y., Huang, C.-H., Du, D.-Z.: Minimum connected dominating sets and maximal independent sets in unit disk graphs. Networks (submitted)

  44. Zhang Z., Gao X., Wu W.: Algorithms for connected set cover problem and fault-tolerant connected set cover problem. Theor. Comput. Sci 410, 812–817 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  45. Zhang, Z., Gao, X., Wu, W., Du, D.-Z.: A PTAS for minimum connected dominating set in 3-dimensional Wireless sensor networks. J. Glob. Optim. 45(3), (2009)

  46. Zong C.: Shere Packings. Springer, New York (1999)

    Google Scholar 

  47. Zou, F., Wang, Y., Li, X., Xu, X., Du, H., Wan, P., Wu, W.: New approximations for minimum-weighted dominating set and minimum-weighted connected dominating set on unit disk graphs. Theor. Comput. Sci. (to appear)

  48. Zou, F., Li, X., Kim, D., Wu, W.: A constant approximation algorithm for node-weighted Steiner tree in unit disk graphs. J. Comb. Optim. (to appear)

  49. Zou, F., Li, X., Kim, D., Wu, W.: Minimum connected dominating set in 3-dimensional wireless network. Optim. Methods Softw. (to appear)

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Authors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, Richardson, TX, 75080, USA

    Weili Wu, Xiaofeng Gao & Ding-Zhu Du

  2. University of Florida, Gainesville, FL, 32611, USA

    Panos M. Pardalos

Authors
  1. Weili Wu
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  2. Xiaofeng Gao
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  3. Panos M. Pardalos
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  4. Ding-Zhu Du
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Correspondence to Xiaofeng Gao.

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Wu, W., Gao, X., Pardalos, P.M. et al. Wireless networking, dominating and packing. Optim Lett 4, 347–358 (2010). https://doi.org/10.1007/s11590-009-0151-8

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