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Whom to Befriend to Influence People

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Structural Information and Communication Complexity (SIROCCO 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9988))

Abstract

Alice wants to join a new social network, and influence its members to adopt a new product or idea. Each person v in the network has a certain threshold t(v) for activation, i.e. adoption of the product or idea. If v has at least t(v) activated neighbors, then v will also become activated. If Alice wants to activate the entire social network, whom should she befriend? We study the problem of finding the minimum number of links that Alice should form to people in the network, in order to activate the entire social network. This Minimum Links Problem has applications in viral marketing and the study of epidemics. We show that the solution can be quite different from the related and widely studied Target Set Selection problem. We prove that the Minimum Links problem is NP-complete, in fact it is hard to approximate to within an \(\epsilon \ln n\) factor for some constant \(\epsilon \), even for graphs with degree 3 and with threshold at most 2. In contrast, we give linear time algorithms to solve the problem for trees, cycles, and cliques, and give precise bounds on the number of links needed.

Research supported by NSERC, Canada.

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Authors and Affiliations

  1. Department of Computer Science and Operational Research, Université de Montréal, Montréal, Canada

    Manuel Lafond

  2. Department of Computer Science and Software Engineering, Concordia University, Montréal, Canada

    Lata Narayanan & Kangkang Wu

Authors
  1. Manuel Lafond
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  2. Lata Narayanan
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  3. Kangkang Wu
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Correspondence to Lata Narayanan .

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Editors and Affiliations

  1. Aalto University, Espoo, Finland

    Jukka Suomela

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Lafond, M., Narayanan, L., Wu, K. (2016). Whom to Befriend to Influence People. In: Suomela, J. (eds) Structural Information and Communication Complexity. SIROCCO 2016. Lecture Notes in Computer Science(), vol 9988. Springer, Cham. https://doi.org/10.1007/978-3-319-48314-6_22

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  • DOI: https://doi.org/10.1007/978-3-319-48314-6_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48313-9

  • Online ISBN: 978-3-319-48314-6

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