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Some results on the target set selection problem

Author

Listed:
  • Chun-Ying Chiang

    (National Central University)

  • Liang-Hao Huang

    (National Central University)

  • Bo-Jr Li

    (National Sun Yat-sen University)

  • Jiaojiao Wu

    (National Sun Yat-sen University)

  • Hong-Gwa Yeh

    (National Central University)

Abstract

In this paper we consider a fundamental problem in the area of viral marketing, called Target Set Selection problem. We study the problem when the underlying graph is a block-cactus graph, a chordal graph or a Hamming graph. We show that if G is a block-cactus graph, then the Target Set Selection problem can be solved in linear time, which generalizes Chen’s result (Discrete Math. 23:1400–1415, 2009) for trees, and the time complexity is much better than the algorithm in Ben-Zwi et al. (Discrete Optim., 2010) (for bounded treewidth graphs) when restricted to block-cactus graphs. We show that if the underlying graph G is a chordal graph with thresholds θ(v)≤2 for each vertex v in G, then the problem can be solved in linear time. For a Hamming graph G having thresholds θ(v)=2 for each vertex v of G, we precisely determine an optimal target set S for (G,θ). These results partially answer an open problem raised by Dreyer and Roberts (Discrete Appl. Math. 157:1615–1627, 2009).

Suggested Citation

  • Chun-Ying Chiang & Liang-Hao Huang & Bo-Jr Li & Jiaojiao Wu & Hong-Gwa Yeh, 2013. "Some results on the target set selection problem," Journal of Combinatorial Optimization, Springer, vol. 25(4), pages 702-715, May.
    • Handle: RePEc:spr:jcomop:v:25:y:2013:i:4:d:10.1007_s10878-012-9518-3
    DOI: 10.1007/s10878-012-9518-3
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    Citations

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    Cited by:

    1. Haining Jiang, 2020. "Target Set Selection on generalized pancake graphs," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(2), pages 379-389, June.
    2. Boris Brimkov & Derek Mikesell & Illya V. Hicks, 2021. "Improved Computational Approaches and Heuristics for Zero Forcing," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1384-1399, October.
    3. Chun-Ying Chiang & Wei-Ting Huang & Hong-Gwa Yeh, 2016. "Dynamic monopolies and feedback vertex sets in cycle permutation graphs, generalized Petersen graphs and torus cordalis," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 815-832, February.
    4. Brimkov, Boris & Fast, Caleb C. & Hicks, Illya V., 2019. "Computational approaches for zero forcing and related problems," European Journal of Operational Research, Elsevier, vol. 273(3), pages 889-903.
    5. Xianliang Liu & Zishen Yang & Wei Wang, 2021. "The t-latency bounded strong target set selection problem in some kinds of special family of graphs," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 105-117, January.

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