http://swrc.ontoware.org/ontology#TechnicalReport
Computational Complexity of Competitive Diffusion on (Un)weighted Graphs
en
Tohoku University
Japan Advanced Institute of Science and Technology
Kobe University
Tohoku University
Tohoku University
Yamagata University
Japan Advanced Institute of Science and Technology
Iwate University
Tohoku University
Takehiro Ito
Yota Otachi
Toshiki Saitoh
Hisayuki Satoh
Akira Suzuki
Kei Uchizawa
Ryuhei Uehara
Katsuhisa Yamanaka
Xiao Zhou
Consider an undirected graph modeling a 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 player chooses a vertex as a seed to propagate his/her opinion, and then it spreads along the edges in the graph. The objective of every player is to maximize the number of infected vertices. In this paper, we investigate a problem of asking whether a pure Nash equilibrium exists in the game on unweighed and weighted graphs. 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. We then show that the problem for forest of paths with arbitrary weights is solvable in pseudo-polynomial time. Moreover, we prove that the problem is solvable in polynomial time for chain graphs, cochain graphs, and threshold graphs with arbitrary integer weights.
Consider an undirected graph modeling a 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 player chooses a vertex as a seed to propagate his/her opinion, and then it spreads along the edges in the graph. The objective of every player is to maximize the number of infected vertices. In this paper, we investigate a problem of asking whether a pure Nash equilibrium exists in the game on unweighed and weighted graphs. 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. We then show that the problem for forest of paths with arbitrary weights is solvable in pseudo-polynomial time. Moreover, we prove that the problem is solvable in polynomial time for chain graphs, cochain graphs, and threshold graphs with arbitrary integer weights.
AN1009593X
研究報告アルゴリズム（AL）
2015-AL-154
8
1-6
2015-09-21
2188-8566