## 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).

Original language | English |
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Pages (from-to) | 702-715 |

Number of pages | 14 |

Journal | Journal of Combinatorial Optimization |

Volume | 25 |

Issue number | 4 |

DOIs | |

State | Published - May 2013 |

## Keywords

- Block graph
- Block-cactus graph
- Chordal graph
- Diffusion of innovations
- Dynamic monopoly
- Hamming graph
- Irreversible spread of influence
- Social networks
- Target set selection
- Tree
- Viral marketing