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Connected Dominating Set: Theory and Applications pp 1–9Cite as

Introduction

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 77))

Abstract

In this chapter, we introduce basic concepts, fundamental results and applications of connected dominating sets.

Most practical questions can be reduced to problems

of largest and smallest magnitudes… and it is only by

solving these problems that we can satisfy the requirements

of practice which always seeks the best, the most convenient.

P.L. Čebyšev

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References

  1. Akyildiz, I.F., Pompili, D., Melodia, T.: Underwater acoustic sensor networks: research challenges. Ad Hoc Network 3(3), 257–279 (2005)

    Article  Google Scholar 

  2. Ambühl, C., Erlebach, T., Mihalák, M., Nunkesser, M.: Constant-approximation for minimum-weight (connected) dominating sets in unit disk graphs. Proceedings of the 9th International Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX 2006). Lecture Notes in Computer Science, vol. 4110 pp. 3–14. Springer, Berlin (2006)

    Google Scholar 

  3. Baker, B.S.: Approximation algorithms for NP-complete problems on planar graphs. J. ACM 41(1), 153–180 (1994)

    Article  MATH  Google Scholar 

  4. Baudis, G., Gröpl, C., Hougardy, S., Nierhoff, T., Prömel, H.J.: Approximating minimum spanning sets in hypergraphs and polymatroids. Technical Report, Humboldt-Universitt zu Berlin (2000)

    Google Scholar 

  5. Benini, L., Castelli, G., Macii, A., Poncino, M., Scarsi, R.: A discrete-time battery model for high-level power estimation. Proceedings of DATE, pp. 35–39 (2000)

    Google Scholar 

  6. Berman, P., Calinescu, G., Shah, C., Zelikovsky, A.: Power efficient monitoring management in sensor networks. IEEE Wireless Communication and Networking Conference (WCNC’04), Atlanta, pp. 2329–2334 (2004)

    Google Scholar 

  7. Berman, P., Calinescu, G., Shah, C., Zelikovsky, A.: Efficient energy management in sensor networks. In: Xiao, Y., Pan, Y. (eds.) Ad Hoc and Sensor Networks, Wireless Networks and Mobile Computing, vol. 2. Nova Science Publishers, New York (2005)

    Google Scholar 

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

    Google Scholar 

  9. Butenko, S., Kahruman-Anderoglu, S., Ursulenko, O.: On connected domination in unit ball graphs. Optim. Lett. 5(2), 195–205 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Byrka, J., Grandoni, F., Rothvoss, T., Sanita, L.: An improved LP-based approximation for Steiner tree. STOC’10, pp. 583–592 (2010)

    Google Scholar 

  11. Calinescu, G., Ellis, R.: On the lifetime of randomly deployed sensor networks. DialM-POMC the Fifth ACM SIGACTSIGOPS International Workshop on Foundation of Mobile Computing (2008)

    Google Scholar 

  12. Calinescu, G., Kapoor, S., Olshevsky, A., Zelikovsky, A.: Network lifetime and power assignment in ad-hoc wireless networks. Proceedings of European Symposium on Algorithms (ESA’03), Lecture Notes in Computer Science, vol. 2832, pp. 114–126 (2003)

    Article  MathSciNet  Google Scholar 

  13. Cardei, M., Du, D.-Z.: Improving wireless sensor network lifetime through power aware organization. ACM Wireless Network. 11(3), 333–340 (2005)

    Article  Google Scholar 

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

    Google Scholar 

  15. Cardei, M., Thai, M., Li, Y., Wu, W.: Energy-efficient target coverage in wireless sensor networks. IEEE INFOCOM, pp. 1976–1984 (2005)

    Google Scholar 

  16. Cardei, M., MacCallum, D., Cheng, X., Min, M., Jia, X., Li, D., Du, D.-Z.: Wireless sensor networks with energy efficient organization. J. Interconnect. Networks 3(3–4), 213–229 (2002)

    Article  Google Scholar 

  17. 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 (2002)

    Google Scholar 

  18. Cheng, M.X., Gong, X.: Maximum lifetime coverage preserving scheduling algorithms in sensor networks. J. Global Optim. 51(3), 447–462 (2011)

    Article  MATH  Google Scholar 

  19. Cheng, M.X., Ruan, L., Wu, W.: Achieving minimum coverage breach under bandwidth constraints in wireless sensor networks. INFOCOM, pp. 2638–2645 (2005)

    Google Scholar 

  20. Cheng, M.X., Ruan, L., Wu, W.: Coverage breach problems in bandwidth-constrained sensor networks. TOSN 3(2), 12 (2007)

    Article  Google Scholar 

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

    Article  Google Scholar 

  22. 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(2), 202–208 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  23. Chvátal, V.: A greedy heuristic for the set-covering problem. Math. Oper. Res. 4(3), 233–235 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  24. Clark, B.N., Colbourn, C.J., Johnson, D.S.: Unit disk graphs. Disc. Math. 86(1–3), 165–177 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  25. Colbourn, C.J., Stewart, L.K.: Permutation graphs: connected domination and Steiner trees. Disc. Math. 86(1–3), 179–189 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  26. Dai, F., Wu, J.: An extended localized algorithm for connected dominating set formation in ad hoc wireless networks. IEEE Trans. Parallel Distrib. Syst. 15(10), 908–920 (2004)

    Article  Google Scholar 

  27. 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  MathSciNet  MATH  Google Scholar 

  28. Deering, S., Farinacci, D., Jacobson, V., Lui, C.-G., Wei, L.: An architecture for wide area multicast routing. In: Proceedings of ACM SIGCOMM 1994, pp. 126–135 (1994)

    Article  Google Scholar 

  29. Ding, L., Wu, W., Willson, J.K., Du, H., Lee, W.: Construction of directional virtual backbones with minimum routing cost in wireless networks. In: 30th Annual Joint Conference of IEEE Communication and Computer Society (INFOCOM), pp. 1557–1565 (2011)

    Google Scholar 

  30. Ding, L., Wu, W., Willson, J.K., Du, H., Lee, W.: Efficient virtual backbone construction with routing cost constraint in wireless networks using directional antennas. IEEE Trans. Mobile Comput. 11(7), 1102–1112 (2012)

    Article  Google Scholar 

  31. Ding, L., Gao, X., Wu, W., Lee, W., Zhu, X., Du, D.-Z.: An exact algorithm for minimum CDS with shortest path constraint in wireless networks. Optim. Lett. (2010) published online

    Google Scholar 

  32. Ding, L., Gao, X., Wu, W., Lee, W., Zhu, Xu, Du, D.-Z.: Distributed construction of connected dominating sets with minimum routing cost in wireless network. In: Proceedings of the 30th International Conference on Distributed Computing Systems (ICDCS), pp. 448–457 (2010)

    Google Scholar 

  33. Ding, L., Wu, W., Willson, J.K., Du, H., Lee, W., Du, D.-Z.: Efficient algorithms for topology control problem with routing cost constraints in wireless networks. IEEE. Trans. Parallel. Distr. Syst. 22(10), 1601–1609 (2011)

    Article  Google Scholar 

  34. Ding, L., Wu, W., Willson, J.K., Wu, L., Lu, Z., Lee, W.: Constant-approximation for target coverage problem in wireless sensor networks. In: Proceedings of the 31st Annual Joint Conference of IEEE Communication and Computer Society (INFOCOM) (2012)

    Google Scholar 

  35. Douglas, R.J.: NP-completeness and degree restricted spanning trees. Disc. Math. 105(1–3), 41–47 (1992)

    Article  MATH  Google Scholar 

  36. Du, D.-Z., Ko, K.-I., Hu, X.: Design and Analysis of Approximation Algorithms. Springer, Berlin (2011)

    Google Scholar 

  37. Du, H., Pardalos, P.M., Wu, W., Wu, L.: Maximum lifetime connected coverage with two active-phase sensors. J. Global Optim. (2012), on line

    Google Scholar 

  38. Du, D.-Z., Thai, M.Y., Li, Y., Liu, D., Zhu, S.: Strongly connected dominating sets in wireless sensor networks with unidirectional links. APWeb, pp. 13–24 (2006)

    Google Scholar 

  39. Du, H., Wu, W., Ye, Q., Li, D., Lee, W., Xu, X.: CDS-based virtual backbone construction with guaranteed routing cost in wireless sensor networks. IEEE Trans. Parallel Distr. Syst., to appear

    Google Scholar 

  40. Du, D.-Z., Graham, R.L., Pardalos, P.M., Wan, P.J., Wu, W., Zhao, W.: Analysis of greedy approximation with nonsubmodular potential functions. In: Proceedings of SODA (2008)

    Google Scholar 

  41. Du, H., Ye, Q., Zhong, J., Wang, A., Lee, W., Park, H.: PTAS for minimum connected dominating set with routing cost constraint in wireless sensor networks. In: 4th Annual International Conference on Combinatorial Optimization and Applications (COCOA) (2010)

    Google Scholar 

  42. Du, H., Wu, W., Lee, W., Liu, Q., Zhang, Z., Du, D.-Z.: On minumum submodular cover with submodular cost. J. Global Optim. 50(2), 229–234 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  43. 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 wireless sensor networks. INFOCOM, pp. 1737–1744 (2011)

    Google Scholar 

  44. Duchet, P., Meyniel, H.: On Hadwiger’s number and stability numbers. Annal. Disc. Math. 13, 71–74 (1982)

    MathSciNet  MATH  Google Scholar 

  45. Eriksson, H.: MBone: the multicast backbone. Commun. ACM (1994)

    Google Scholar 

  46. Erlebach, T., Mihalák, M.: A (4 + ε)-approximation for the minimum-weight dominating set problem in unit disk graphs. WAOA, pp. 135–146 (2009)

    Google Scholar 

  47. Feige, U.: A threshold of lnn for approximating set cover. J. ACM 45(4), 634–652 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  48. Feige, U., Halldórsson, M.M., Kortsarz, G., Srinivasan, A.: Approximating the domatic number. SIAM J. Comput. 32(1), 172–195 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  49. Fodor, F.: The densest packing of 13 congruent circles in a circle. Beitrage Algebra Geom. 44(2), 431–440 (2003)

    MathSciNet  MATH  Google Scholar 

  50. Folkman, J.H., Graham, R.L.: A packing inequality for compact convex subsets of the plane. Canad. Math. Bull. 12, 745–752 (1969)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  52. Fujito, T.: Approximation algorithms for submodular set cover with application, IEICE Trans. Inf. Syst. E83-D(3), 480–487 (2000)

    Google Scholar 

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

    Google Scholar 

  54. Gao, X., Wang, Y., Li, X., Wu, W.: Analysis on theoretical bounds of approximating dominating set problems. Disc. Math. Algorithms Appl. 1(1), 71–84 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  55. Garg, N., Könemann, J.: Faster and simpler algorithms for multicommodity flows and other fractional packing problems. In: Proceedings of 39th Annual Symposium on the Foundations of Computer Science (FOCS), pp. 300–309 (1998)

    Google Scholar 

  56. Garey, M.R., Johnson, D.S.: The rectilinear Steiner tree problem is NP-complete. SIAM J. Appl. Math. 32, 826–834 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  57. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman and Sons, San Francisco, CA (1979)

    MATH  Google Scholar 

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

    Google Scholar 

  59. Gibson, M., Pirwani, I.: Algorithms for dominating set in disk graphs: breaking the logn barrier. Algorithms–ESA, pp. 243–254 (2010)

    Google Scholar 

  60. Green, P.E.: Fiber-Optic Networks. Prentical-Hall, Cambrige, MA (1992)

    Google Scholar 

  61. Groemer, H.: Über die Einlagerung von Kreisen in einen konvexen Bereich. Math. Z. 73, 285–294 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  62. Guha, S., Khuller, S.: Approximation algorithms for connected dominating sets. Algorithmica 20(4), 374–387 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  63. Guha, S., Khuller, S.: Improved methods for approximating node weighted Steiner trees and connected dominating sets. Springer Lect. Notes Comput. Sci. 1530, 54–66 (1998)

    Article  Google Scholar 

  64. Hahn, R., Reichl, H.: Batteries and power supplies for wearable and ubiquitous computing. In: Proceedings of the 3rd International Symposium on Wearable Computers (1999)

    Google Scholar 

  65. Hoppe, R.: Bemerkungen de redaktion. Grunert Arch. Math. Phys. 56, 307–312 (1874)

    Google Scholar 

  66. Huang, Y., Gao, X., Zhang, Z., Wu, W.: A better constant-factor approximation for weighted dominating set in unit disk graph. J. Combin. Optim. 18(2), 179–194 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  67. 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. 20(2), 147–157 (2009)

    Article  Google Scholar 

  68. 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)

    Article  Google Scholar 

  69. Klein, P.N., Ravi, R.: A nearly best-possible approximation for node-weighted Steiner trees. J. Algorithms 19, 104–115 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  70. Kuhn, F., Zollinger, A.: Ad-hoc networks beyond unit disk graphs. In: Proceedings of the Joint Workshop of Foundation of Mobile Computing (DIALM-POMC) (2003)

    Google Scholar 

  71. Laskar, R., Pfaff, J.: Domination and irredundance in split graphs. Technical Report 430, Department of Mathematical Sciences, Clemson University (1983)

    Google Scholar 

  72. Li, M., Wan, P.J., Yao, F.F.: Tighter approximation bounds for minimum CDS in wireless ad hoc networks. ISAAC’2009. Lecture Notes in Computer Science, vol. 5878, pp. 699–709 (2009)

    Article  Google Scholar 

  73. Li, D., Du, X., Hu, X., Jia, X.: Minimizing number of wavelengths in multicast routing trees in WDM networks. Networks 35(4), 260–265 (2000)

    Article  Google Scholar 

  74. Li, Y., Thai, M.T., Wang, F., Du, D.-Z.: On the construction of a strongly connected broadcast arborescence with bounded transmission delay. IEEE Trans. Mobile Comput. 5(10), 1460–1470 (2006)

    Article  Google Scholar 

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

    Article  Google Scholar 

  76. Li, D., Du, H., Wan, P.-J., Gao, X., Zhang, Z., Wu, W.: Minimum power strongly connected dominating sets in wireless networks. In: Proceedings of the 2008 International Conference on Wireless Networks (ICWN’08) (2008)

    Google Scholar 

  77. Li, D., Du, H., Wan, P.-J., Gao, X., Zhang, Z., Wu, W.: Construction of strongly connected dominating sets in asymmetric multihop wireless networks. Theoret. Comput. Sci. 410(8–10), 661–669 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  78. Liu, Q., Li, X., Wu, L., Du, H., Zhang, Z., Wu, W., Xu, Y.: A new proof for Zassenhaus–Groemer–Oler inequality. Disc. Math. Algorithms Appl. (2012), to appear

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  80. Moscibroda, T., Wattenhofer, R.: Maximizing the lifetime of dominating sets. In: Proceedings of the 5th IEEE International Workshop on Algorithms for Wireless, Mobile, Ad hoc and Sensor Networks (2005)

    Google Scholar 

  81. Mukherjee, B.: WDM-based local lightwave networks Part I: single-hop system. IEEE Networks 3, 12–26 (1992)

    Article  Google Scholar 

  82. Mukherjee, B.: WDM-based local lightwave networks Part II: multihop system. IEEE Networks 4, 22–32 (1992)

    Google Scholar 

  83. Mustafa, N., Ray, S.: Improved results on geometric hitting set problems. Disc. Comput. Geometry 44(4), 883–895 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  84. Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley, New York (1999)

    MATH  Google Scholar 

  85. Oler, N.: An inequality in the geometry of numbers. Acta Math. 105, 19–48 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  86. Pandit, S., Pemmaraju, S.V., Varadarajan, K.R.: Approximation algorithms for domatic partitions of unit disk graphs. In: Dinur, L. et al. (eds.) APPROX and RANDOM 2009. Lecture Notes in Computer Science, vol. 5687, pp. 312–325 (2009)

    Article  MathSciNet  Google Scholar 

  87. Ramamurthy, B., Iness, J., Mukherjee, B.: Minimizing the number of optical amplifiers needed to support a multi-wavelength optical LAN/MAN. In: Proceedings of IEEE INFOCOM’97, pp. 261–268 (1997)

    Google Scholar 

  88. Ramaswami, R., Sasaki, G.: Multiwavelength optical networks with limited wavelength conversion. IEEE/ACM Trans. Networking 6(6), 744–754 (1998)

    Article  Google Scholar 

  89. Raz, R., Safra, S.: A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP. In: Proceedings of 28th STOCS (1997)

    Google Scholar 

  90. Ruan, L., Du, D.-Z., Hu, X., Jia, X., Li, D.: Approximations for color-covering problems. In: Proceedings of 1st International Congress of Chinese Mathematicians, pp. 503–507. Beijing, China (1998)

    Google Scholar 

  91. Ruan, L., Du, D.-Z., Hu, X., Jia, X., Li, D., Sun, Z.: Converter placement supporting broadcast in WDM optical networks. IEEE Trans. Comput. 50(7), 750–758 (2001)

    Article  MathSciNet  Google Scholar 

  92. Ruan, L., Du, H., Jia, X., Wu, W., Li, Y., Ko, K.-I.: A greedy approximation for minimum connected dominating set. Algorithmca, 329(1–3), 325–330 (2004)

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  94. Sampathkumar, E., Walikar, H.B.: The connected domination number of a graph. J. Math. Phys. Sci. 13(6), 607–613 (1979)

    MathSciNet  MATH  Google Scholar 

  95. 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 (1998)

    Google Scholar 

  96. Slijepcevic, S., Potkonjak, M.: Power efficient organization of wireless sensor networks. IEEE International Conference on Communications, pp. 472–476 (2001)

    Google Scholar 

  97. Solis-Oba, R.: 2-approximation algorithm for finding a spanning tree with maximum number of leaves. In: Proceedings of 6th European Symposium on Algorithms (ESA’98). Lecture Notes in Computer Science, vol. 1461, pp. 441–452. Springer, Berlin (1998)

    Google Scholar 

  98. Srinivasan, A., Wu, J.: TRACK: A novel connected dominating set based sink mobility model for WSNs. ICCCN, pp. 664–671 (2008)

    Google Scholar 

  99. 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 (2001)

    Google Scholar 

  100. Sum, J., Wu, J., Ho, K.: Analysis on a localized pruning method for connected dominating sets. J. Inf. Sci. Eng. 23(4), 1073–1086 (2007)

    MathSciNet  Google Scholar 

  101. Thai, M.T., Du, D.-Z.: Connected dominating sets in disk graphs with bidirectional links. IEEE Commun. Lett. 10(3), 138–140 (2006)

    Article  Google Scholar 

  102. Thai, M.Y., Wang, F., Liu, D., Zhu, S., Du, D.-Z.: Connected dominating sets in wireless networks with different communication ranges. IEEE Trans. Mobile Comput. 6(7), 721–730 (2007)

    Article  Google Scholar 

  103. Vahdatpour, A., Dabiri, F., Moazeni, M., Sarrafzadeh, M.: Theoretical bound and practical analysis of connected dominating set in ad hoc and sensor networks. In: Proceedings of 22nd International Symposium on Distributed Computing (DISC), pp. 481–495 (2008)

    Google Scholar 

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

    Google Scholar 

  105. Wan, P.-J., Alzoubi, K.M., Frieder, O.: A simple heuristic for minimum connected dominating set in graphs. Int. J. Found. Comput. Sci. 14(2), 323–333 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  107. Wan, P.-J., Xu, X., Wang, Z.: Wireless coverage with disparate ranges. ACM Mobihoc (2011)

    Google Scholar 

  108. Wan, P.-J., Du, D.-Z., Pardalos, P.M., Wu, W.: Greedy approximations for minimum submodular cover with submodular cost. Comput. Optim. Appl. 45(2), 463–474 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  109. Wan, P.J., Huang, S.C.-H., Wang, L., Wan, Z., Jia, X.: Minimum-latency aggregation scheduling in multihop wireless networks. ACM MOBIHOC (2009)

    Google Scholar 

  110. Wan, P.-J., Wang, Z., Wan, Z., Huang, S.C.-H., Liu, H.: Minimum-latency schedulings for group communications in multi-channel multihop wireless networks. WASA (2009)

    Google Scholar 

  111. Wang, F., Thai, M.T., Du, D.-Z.: On the construction of 2-connected virtual backbone in wireless networks. IEEE Trans. Wireless Commun. 8(3), 1230–1237 (2009)

    Article  Google Scholar 

  112. Wang, L., Wan, P.-J., Yao, F.F.: Minimum CDS in multihop wireless networks with disparate communication ranges, WASA (2010)

    Google Scholar 

  113. White, K., Parber, M., Pulleyblank, W.: Steiner trees, connected domination and strongly chordal graphs. Networks 15(1), 109–124 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  114. Willson, J.K., Ding, L., Wu, W., Wu, L., Lu, Z., Lee, W.: A better constant-approximation for coverage problem in wireless sensor networks, preprint.

    Google Scholar 

  115. Willson, J.K., Gao, X., Qu, Z., Zhu, Y., Li, Y., Wu, W.: Efficient distributed algorithms for topology control problem with shortest path constraints. Disc. Math. Algorithms Appl. 1, 437–461 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  116. Wolsey, L.A.: An analysis of the greedy algorithm for submodular set covering problem. Combinatorica 2(4), 385–393 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  117. 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)

    Google Scholar 

  118. Wu, J., Dai, F.: Virtual backbone construction in MANETs using adjustable transmission ranges. IEEE Trans. Mob. Comput. 5(9), 1188–1200 (2006)

    Article  Google Scholar 

  119. Wu, J., Gao, M., Stojmenovic, I.: On calculating power-aware connected dominating sets for efficient routing in ad hoc wireless networks. ICPP pp. 346–356 (2001)

    Google Scholar 

  120. Wu, J., Wu, B., Stojmenovic, I.: Power-aware broadcasting and activity scheduling in ad hoc wireless networks using connected dominating sets. Wireless Commun. Mobile Comput. 3(4), 425–438 (2003)

    Article  Google Scholar 

  121. Wu, J., Dai, F., Yang, S.: Iterative local solutions for connected dominating set in ad hoc wireless networks, MASS (2005)

    Google Scholar 

  122. Wu, J., Lou, W., Dai, F.: Extended multipoint relays to determine connected dominating sets in MANETs. IEEE Trans. Comput. 55(3), 347–337 (2006)

    Article  Google Scholar 

  123. 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)

    Article  MathSciNet  MATH  Google Scholar 

  124. Xing, K., Cheng, W., Park, E.K., Rotenstreich, S.: Distributed connected dominating set construction in geometric k-disk graphs. IEEE ICDCS, pp. 673–680 (2008)

    Google Scholar 

  125. Zassenhaus, H.: Modern development in the geometry of numbers. Bull. Amer. Math. Soc. 67, 427–439 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  126. Zhang, Y., Li, W.: Modeling and energy consumption evaluation of a stochastic wireless sensor networks. preprint (2011)

    Google Scholar 

  127. Zhang, Z., Gao, X., Wu, W., Du, D.-Z.: A PTAS for minimum connected dominating set in 3-dimensional wireless sensor networks. J. Global Optim. 45(3), 451–458 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  128. Zhang, N., Shin, I., Zou, F., Wu, W., Thai, M.T.: Trade-off scheme for fault tolerant connected dominating sets on size and diameter. FOWANC, pp. 1–8 (2008)

    Google Scholar 

  129. Zhao, Y., Wu, J., Li, F., Lu, S.: VBS: Maximum lifetime sleep scheduling for wireless sensor networks using virtual backbones, INFOCOM pp. 366–370 (2010)

    Google Scholar 

  130. Zhong, C.: Sphere Packing. Springer, Berlin (1999)

    Google Scholar 

  131. Zhong, X., Wang, J., Hu, N.: Connected dominating set in 3-dimensional space for ad hoc network. In: Proceedings of IEEE Wireless Communications and Networking Conference (WCNC’07) (2007)

    Google Scholar 

  132. Zou, F., Li, X., Kim, D., Wu, W.: Construction of minimum connected dominating set in 3-dimensional wireless networks. In: Proceedings of Third International Conference on Wireless Algorithms, Systems and Applications (WASA 08) (2008)

    Google Scholar 

  133. Zou, F., Li, X., Gao, S., Wu, W.: Node-weighted Steiner tree approximation in unit disk graphs. J. Combin. Optim. 18(4), 342–349 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  134. Zou, F., Wang, Y., Xu, X., Du, H., Li, X., Wan, P., Wu, W.: New approximations for weighted dominating sets and connected dominating sets in unit disk graphs. Theoret. Comput. Sci. 412(3), 198–208 (2011)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

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

    Ding-Zhu Du

  2. Department of Computer Science, Illinois Institute of Technology, Chicago, IL, USA

    Peng-Jun Wan

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  1. Ding-Zhu Du
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  2. Peng-Jun Wan
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Du, DZ., Wan, PJ. (2013). Introduction. In: Connected Dominating Set: Theory and Applications. Springer Optimization and Its Applications, vol 77. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5242-3_1

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