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On Finding Better Friends in Social Networks

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Book cover Stabilization, Safety, and Security of Distributed Systems (SSS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7596))

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Abstract

We study the dynamics of a social network. Each node has to decide locally which other node it wants to befriend, i.e., to which other node it wants to create a connection in order to maximize its welfare, which is defined as the sum of the weights of incident edges. This allows us to model the cooperation between nodes where every node tries to do as well as possible. With the limitation that each node can only have a constant number of friends, we show that every local algorithm is arbitrarily worse than a globally optimal solution. Furthermore, we show that there cannot be a best local algorithm, i.e., for every local algorithm exists a social network in which the algorithm performs arbitrarily worse than some other local algorithm. However, one can combine a number of local algorithms in order to be competitive with the best of them. We also investigate a slightly different valuation variant. Nodes include another node’s friends for their valuation. There are scenarios in which this does not converge to a stable state, i.e., the nodes switch friends indefinitely.

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Author information

Authors and Affiliations

  1. Computer Engineering and Networks Lab (TIK), ETH Zurich, Switzerland

    Philipp Brandes & Roger Wattenhofer

Authors
  1. Philipp Brandes
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  2. Roger Wattenhofer
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Editor information

Editors and Affiliations

  1. School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, 699 South Mill Avenue, 85281, Tempe, AZ, USA

    Andréa W. Richa

  2. Department of Computer Science, University of Paderborn, Fürstenallee 11, 33102, Paderborn, Germany

    Christian Scheideler

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Brandes, P., Wattenhofer, R. (2012). On Finding Better Friends in Social Networks. In: Richa, A.W., Scheideler, C. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2012. Lecture Notes in Computer Science, vol 7596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33536-5_26

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  • DOI: https://doi.org/10.1007/978-3-642-33536-5_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33535-8

  • Online ISBN: 978-3-642-33536-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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