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\(k\)-Power domination in block graphs

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Abstract

The power system monitoring problem asks for as few as possible measurement devices to be put in an electric power system. The problem has a graph theory model involving power dominating set in graphs. The concept of \(k\)-power domination, first introduced by Chang et al. (Discret Appl Math 160:1691–1698, 2012), is a common generalization of domination and power domination. In this paper, we present a linear-time algorithm for \(k\)-power domination in block graphs.

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References

  • Aazami A (2010) Domination in graphs with bounded propagation: algorithms, and hardness results. J Comb Optim 19:429–456

  • Aazami A, Stilp MD (2009) Approximation algorithms and hardness for domination with propagation. SIAM J Discret Math 23:1382–1399

    Article  MathSciNet  MATH  Google Scholar 

  • Baldwin TL, MiLi L, Boisen MB Jr, Adapa A (1993) Power system observability with minimal phasor measurement placement. IEEE Trans Power Syst 8:707–715

    Article  Google Scholar 

  • Chang GJ (1998) Algorithmic aspects of domination in graphs. In: Du DZ, Pardalos PM (eds) Handbook of combinatorial optimization, vol 3. Kluwer Academic Publishers, Boston

    Google Scholar 

  • Chang GJ (1989) Total domination in block graphs. Oper Res Lett 8:53–57

    Article  MathSciNet  MATH  Google Scholar 

  • Chang GJ, Dorbec P, Montassier M, Raspaud A (2012) Generalized power domination of graphs. Discret Appl Math 160:1691–1698

    Article  MathSciNet  MATH  Google Scholar 

  • Chang GJ, Nemhauser GL (1982) \(R\)-domination on block graphs. Oper Res Lett 1:214–218

    Article  MathSciNet  MATH  Google Scholar 

  • Chen L, Lu C, Zeng Z (2010) Labelling algorithms for paired-domination problems in block and interval graphs. J Comb Optim 19:457–470

    Article  MathSciNet  MATH  Google Scholar 

  • Chen L, Lu C, Zeng Z (2009) A linear-time algorithm for paired-domination problem in strongly chordal graphs. Inf Process Lett 110:20–23

    Article  MathSciNet  MATH  Google Scholar 

  • Cockayne EJ, Goodman SE, Hedetniemi ST (1975) A linear algorithm for the domination number of a tree. Inf Process Lett 4:41–44

    Article  MATH  Google Scholar 

  • Dirac GA (1961) On rigid circuit graphs. Abh Math Sem Univ Hamburg 25:71–76

    Article  MathSciNet  MATH  Google Scholar 

  • Dorbec P, Henning MA, Lowenstein C, Montassier M, Raspaud A (2013) Generalized power domination in regular graphs. SIAM J Discret Math 27:1559–1574

    Article  MathSciNet  MATH  Google Scholar 

  • Dorbec P, Mollard M, Klavžar S, Špacapan S (2008) Power domination in product graphs. SIAM J Discret Math 22:554–567

    Article  MATH  Google Scholar 

  • Dorfling M, Henning MA (2006) A note on power domination in grid graphs. Discret Appl Math 154:1023–1027

    Article  MathSciNet  MATH  Google Scholar 

  • Guo J, Niedermeier R, Raible D (2008) Improved algorithms and complexity results for power domination in graphs. Algorithmica 52:177–202

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Haynes TW, Hedetniemi SM, Hedetniemi ST, Henning MA (2002) Domination in graphs applied to electric power networks. SIAM J Discret Math 15:519–529

    Article  MathSciNet  MATH  Google Scholar 

  • Kneis J, Molle D, Richter S, Rossmanith P (2006) Parameterized power domination complexity. Inform Process Lett 98:145–149

    Article  MathSciNet  MATH  Google Scholar 

  • Liao CS, Lee DT (2005) Power domination problem in graphs. In: Proceedings of 11th Annual International Conference, COCOON 2005, Kunming, China, 2005, In: Lecture notes in computer science, vol 3595, pp 818–828

  • Liao CS, Lee DT (2013) Power domination in circular-arc graphs. Algorithmica 65:443–466

    Article  MathSciNet  MATH  Google Scholar 

  • Wimer TV (1987) Linear algorithms on \(k\)-terminal graphs, Ph.D. Thesis, Clemson University

  • Xu G, Kang L (2011) On the power domination number of the generalized Petersen graphs. J Comb Optim 22:282–291

    Article  MathSciNet  MATH  Google Scholar 

  • Xu G, Kang L, Shan E, Zhao M (2006) Power domination in block graphs. Theor Comput Sci 359:299–305

    Article  MathSciNet  MATH  Google Scholar 

  • Yen WCK (2003) The bottleneck independent domination on the classes of bipartite graphs and block graphs. Inf Sci 157:199–215

    Article  MATH  Google Scholar 

Download references

Acknowledgments

Supported in part by National Natural Science Foundation of China (Nos. 61202021, 11371008, 91230201, 61373028), Shanghai Educational Development Foundation (No. 12CG55), Innovation Program of Shanghai Municipal Education Commission (No. 12YZ120), Science & Technology Program of Shanghai Maritime University (20120105).

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Correspondence to Changhong Lu.

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Wang, C., Chen, L. & Lu, C. \(k\)-Power domination in block graphs. J Comb Optim 31, 865–873 (2016). https://doi.org/10.1007/s10878-014-9795-0

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  • DOI: https://doi.org/10.1007/s10878-014-9795-0

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