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The k-power Domination Problem in Weighted Trees

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Algorithmic Aspects in Information and Management (AAIM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11343))

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Abstract

The power domination problem of the graph comes from how to choose the node location problem of the least phase measurement units in the electric power system. In the actual electric power system, because of the difference in the cost of phase measurement units at different nodes, it is more practical to study the power domination problem with the weighted graph. In this paper, we present a dynamic programming style linear-time algorithm for k-power domination problem in weighted trees.

Supported in part by National Natural Science Foundation of China (No. 11371008) and Science and Technology Commission of Shanghai Municipality (No. 18dz2271000).

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References

  1. Aazami, A.: Domination in graphs with bounded propagation: algorithms, formulations and hardness result. J. Comb. Optim. 19(4), 429–456 (2010)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  3. Baldwin, T.L., Mili, L., Boisen Jr., M.B., Adapa, R.: Power system observability with minimal phasor measurement placement. IEEE Trans. Power Systems. 8, 707–715 (1993)

    Article  Google Scholar 

  4. Brandstadt, A., Kratsch, D.: On domination problems on permutation and other graphs. Theoret. Comput. Sci. 54(2–3), 181–198 (1987)

    Article  MathSciNet  Google Scholar 

  5. Chang, G.J.: Algorithmic aspects of domination in graphs. In: Handbook of Optimization, vol. 3, pp. 339–405 (1998)

    Chapter  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Chang, M.S., Liu, Y.C.: Polynomial algorithms for the weighted perfect domination problems on chordal graphs and split graphs. Inf. Process. Lett. 48(4), 205–210 (1993)

    Article  MathSciNet  Google Scholar 

  8. Chang, M.S., Liu, Y.C.: Polynomial algorithms for weighted perfect domination problems on interval and circular-arc graphs. J. Inf. Sci. Eng. 11, 549–568 (1994)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  12. Haynes, T.W., Hedetniemi, S.M., Hedetniemi, S.T., Henning, M.A.: Domination in graphs applied to electric power networks. SIAM J. Discret. Math. 15, 519–529 (2002)

    Article  MathSciNet  Google Scholar 

  13. Liao, C.-S., Lee, D.-T.: Power domination problem in graphs. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 818–828. Springer, Heidelberg (2005). https://doi.org/10.1007/11533719_83

    Chapter  Google Scholar 

  14. Lu, C., Mao, R., Wang, B.: Power domination in regular claw-free graphs. arXiv preprint arXiv:1808.02613 (2018)

  15. Kratsch, D., Stewart, L.: Domination on cocomparability graphs. Discret. Appl. Math. 63(3), 215–222 (1995)

    Article  Google Scholar 

  16. Natarajan, K.S., White, L.J.: Optimum domination in weighted trees. Inf. Process. Lett. 7(6), 261–265 (1978)

    Article  MathSciNet  Google Scholar 

  17. Novak, T., Zerovnik, J.: Weighted domination number of cactus graphs. Int. J. Appl. Math. 29(4), 401–423 (2016)

    Article  MathSciNet  Google Scholar 

  18. Wimer, T.V.: Linear algorithms on k-terminal graphs. Ph.D. Thesis, Clemson University (1987)

    Google Scholar 

  19. Yen, C.C., Lee, R.: The weighted perfect domination problem. Inf. Process. Lett. 35(6), 295–299 (1990)

    Article  MathSciNet  Google Scholar 

  20. Yeh, H.G., Chang, G.J.: Weighted connected domination and Steiner trees in distance-hereditary graphs. Discret. Appl. Math. 87(1–3), 245–253 (1998)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, People’s Republic of China

    ChangJie Cheng, Changhong Lu & Yu Zhou

Authors
  1. ChangJie Cheng
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  2. Changhong Lu
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  3. Yu Zhou
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Corresponding author

Correspondence to Changhong Lu .

Editor information

Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Shaojie Tang

  2. University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  3. University of California, Davis, Davis, CA, USA

    David Woodruff

  4. Texas A&M University, College Station, TX, USA

    Sergiy Butenko

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Cheng, C., Lu, C., Zhou, Y. (2018). The k-power Domination Problem in Weighted Trees. In: Tang, S., Du, DZ., Woodruff, D., Butenko, S. (eds) Algorithmic Aspects in Information and Management. AAIM 2018. Lecture Notes in Computer Science(), vol 11343. Springer, Cham. https://doi.org/10.1007/978-3-030-04618-7_13

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  • DOI: https://doi.org/10.1007/978-3-030-04618-7_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04617-0

  • Online ISBN: 978-3-030-04618-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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