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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/13758

Title: Competitive Diffusion on Weighted Graphs
Authors: Ito, Takehiro
Otachi, Yota
Saitoh, Toshiki
Satoh, Hisayuki
Suzuki, Akira
Uchizawa, Kei
Uehara, Ryuhei
Yamanaka, Katsuhisa
Zhou, Xiao
Keywords: competitive diffusion
graph class
social network
game theory
Issue Date: 2015-08-05
Publisher: Springer
Magazine name: Lecture Notes in Computer Science
Volume: 9214
Start page: 422
End page: 433
DOI: 10.1007/978-3-319-21840-3_35
Abstract: Consider an undirected and vertex-weighted graph modelinga social network, where the vertices represent individuals, the edges do connections among them, and weights do levels of importance of individuals. In the competitive diffusion game, each of a number of players chooses a vertex as a seed to propagate his/her idea which spreads along the edges in the graph. The objective of every player is to maximize the sum of weights of vertices infected by his/her idea. In this paper, we study a computational problem of asking whether a pure Nash equilibrium exists in a given graph, and present several negative and positive results with regard to graph classes. We first prove that the problem is W[1]-hard when parameterized by the number of players even for unweighted graphs. We also show that the problem is NP-hard even for series-parallel graphs with positive integer weights, and is NP-hard even for forests with arbitrary integer weights. Furthermore, we show that the problem for forests of paths with arbitrary weights is solvable in pseudo-polynomial time; and it is solvable in quadratic time if a given graph is unweighted. We also prove that the problem is solvable in polynomial time for chain graphs, cochain graphs, and threshold graphs with arbitrary integer weights.
Rights: This is the author-created version of Springer, Takehiro Ito, Yota Otachi, Toshiki Saitoh, Hisayuki Satoh, Akira Suzuki, Kei Uchizawa, Ryuhei Uehara, Katsuhisa Yamanaka and Xiao Zhou, Lecture Notes in Computer Science, 9214, 2015, 422-433. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/978-3-319-21840-3_35
URI: http://hdl.handle.net/10119/13758
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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