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Algorithms for the minimum weight k-fold (connected) dominating set problem

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Abstract

In this paper, we study the problem of computing a minimum weight k-fold dominating set (MWkDS) or a minimum weight k-fold connected dominating set (MWkCDS) in a unit ball graph (UBG). Using slab decomposition and dynamic programming, we give two exact algorithms for the computation of MWkDS and MWkCDS which can be executed in polynomial time if the thickness of the graph is bounded above.

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References

  • Alzoubi KM, Wan PJ, Frieder O (2002) New distributed algorithm for connected dominating set in wireless ad hoc networks. In: Proc 35th Hawaii int conf system science, Big Island, Hawaii

    Google Scholar 

  • Blum J, Ding M, Thaeler A, Cheng XZ (2004) Connected dominating set in sensor networks and MANETs. In: Du DZ, Pardalos P (eds) Handbook of combinatorial optimization. Kluwer Academic, Dordrecht, pp 329–369

    Google Scholar 

  • Butenko S, Ursulenko O (2010) On minimum connected dominating set problem in unit-ball graphs. Optim Lett, to appear

  • Cadei M, Cheng X, Du D-Z (2002) Connected domination in ad hoc wireless networks. In: Proc 6th int conf computer science and informatics

    Google Scholar 

  • Cheng XZ, Huang X, Li DY, Wu WL, Du DZ (2003) Polynomial-time approximation scheme for minimum connected dominating set in ad hoc wireless networks. Networks 42:202–208

    Article  MathSciNet  MATH  Google Scholar 

  • Chvátal V (1983) Linear programming. Freeman, San Francisco

    MATH  Google Scholar 

  • Clark BN, Colbourn CJ, Johnson DS (1990) Unit disk graphs. Discrete Math 86:165–177

    Article  MathSciNet  MATH  Google Scholar 

  • Das B, Bharghavan V (1997) Routing in ad hoc networks using minimum connected dominating sets. In: ICC’97, Montreal, Canada, pp 376–380

    Google Scholar 

  • Feige U (1998) A threshold of ln n for approximating set cover. J ACM 45:634–652

    Article  MathSciNet  MATH  Google Scholar 

  • Funke S, Segal M (2006) A simple improved distributed algorithm for minimum CDS in unit disk graphs. ACM Trans Sens Netw 2:444–453

    Article  Google Scholar 

  • Gao B, Yang YH, Ma HY (2004) An efficient approximation scheme for minimum connected dominating set in wireless ad hoc networks. In: IEEE vehicular technology conference No 60, Los Angeles CA

    Google Scholar 

  • Gao XF, Kim DH, Zou F (2009) Coverage and dominating problems in wireless sensor network. In: Yang X et al. (eds) Handbook on sensor networks. Wold Scientific, Singapore

    Google Scholar 

  • Garey MR, Johnson DS (1979) Computers and intractability a guide to the theory of NP-completeness. Freeman, New York

    MATH  Google Scholar 

  • Guha M, Khuller S (1998) Approximation algorithms for connected dominating set. Algorithmica 20:374–387

    Article  MathSciNet  MATH  Google Scholar 

  • Haynes TW, Hedetniemi ST, Slater PJ (1998a) Fundamentals of domination in graphs. Dekker, New York

    MATH  Google Scholar 

  • Haynes TW, Hedetniemi ST, Slater PJ (1998b) Domination in graphs, advanced topics. Dekker, New York

    MATH  Google Scholar 

  • Hunt HB III, Marathe MV, Radhakrishnan V, Ravi SS, Rosenkrantz DJ, Stearns RE (1998) NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs. J Algorithms 26:238–274

    Article  MathSciNet  MATH  Google Scholar 

  • Jia L, Rajaraman R, Suel T (2002) An efficient distributed algorithm for constructing small dominating sets. Distrib Comput 15:193–205

    Article  Google Scholar 

  • Johnson DS (1974) Approximation algorithms for combinatorial problems. J Comput Syst Sci 9:256–278

    Article  MATH  Google Scholar 

  • Kim D, Zhang Z, Li XY, Wang W, Wu WL, Du D-Z (2010) A better approximation algorithm for computing connected dominating sets in unit ball graphs. IEEE Trans Mob Comput 9:1108–1118

    Article  Google Scholar 

  • Kuhn F, Wattenhofer R (2005) Constant-time distributed dominating set approximation. Distrib Comput 17:303–310

    Article  Google Scholar 

  • Lovasz L (1975) On the ratio of optimal integral and fractional covers. Discrete Math 13

  • Min M, Du HW, Jia XH, Huang CX, Huang SCH, Wu WL (2006) Improving construction for connected dominating set with steiner tree in wireless sensor networks. J Glob Optim 35:111–119

    Article  MathSciNet  MATH  Google Scholar 

  • Ruan L, Du HW, Jia XH, Wu WL, Li YS, Ko K (2004) A greedy approximation for minimum connected dominating sets. Theor Comput Sci 329:325–330

    Article  MathSciNet  MATH  Google Scholar 

  • van Leeuwen EJ (2005) Approximation algorithms for unit disk graphs. In: Proceedings of the 31st international workshop on graph-theoretic concepts in computer science

    Google Scholar 

  • Wan PJ, Wang LX, Yao F (2008) Two-phased approximation algorithms for minimum CDS in wireless ad hoc networks. In: The 28th international conference on distributed computing systems, pp 337–344

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Key Laboratory of Data Engineering and Knowledge Engineering, MOE, School of Information, Renmin University of China, Beijing, 100872, China

    Wenkai Ma & Deying Li

  2. College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, China

    Zhao Zhang

Authors
  1. Wenkai Ma
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  2. Deying Li
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  3. Zhao Zhang
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Correspondence to Deying Li.

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Ma, W., Li, D. & Zhang, Z. Algorithms for the minimum weight k-fold (connected) dominating set problem. J Comb Optim 23, 528–540 (2012). https://doi.org/10.1007/s10878-010-9372-0

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  • DOI: https://doi.org/10.1007/s10878-010-9372-0

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