Competitive diffusion on weighted graphs

Takehiro Ito, Yota Otachi, Toshiki Saitoh, Hisayuki Satoh, Akira Suzuki, Kei Uchizawa, Ryuhei Uehara, Katsuhisa Yamanaka, Xiao Zhou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

Consider an undirected and vertex-weighted 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 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.

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings
EditorsFrank Dehne, Jorg-Rudiger Sack, Ulrike Stege
PublisherSpringer Verlag
Pages422-433
Number of pages12
ISBN (Print)9783319218397
DOIs
Publication statusPublished - 2015
Event14th International Symposium on Algorithms and Data Structures, WADS 2015 - Victoria, Canada
Duration: 2015 Aug 52015 Aug 7

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9214
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other14th International Symposium on Algorithms and Data Structures, WADS 2015
CountryCanada
CityVictoria
Period15/8/515/8/7

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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