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).
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The authors would like to thank the anonymous referee for very careful reading and for many constructive suggestions which help to improve the presentation of this paper.
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Second author is partially supported by National Science Council under grant NSC100-2811-M-008-052.
First and fourth authors are partially supported by National Science Council under grant NSC100-2115-M-008-007-MY2.
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Chiang, CY., Huang, LH., Li, BJ. et al. Some results on the target set selection problem. J Comb Optim 25, 702–715 (2013). https://doi.org/10.1007/s10878-012-9518-3
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DOI: https://doi.org/10.1007/s10878-012-9518-3