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Algorithms for influence maximization in socio-physical networks

Author

Listed:
  • Hemant Gehlot

    (Indian Institute of Technology Kanpur)

  • Shreyas Sundaram

    (Purdue University)

  • Satish V. Ukkusuri

    (Purdue University)

Abstract

Given a directed graph (referred to as social network), the influence maximization problem is to find k nodes which, when influenced (or activated), would maximize the number of remaining nodes that get activated under a given set of activation dynamics. In this paper, we consider a more general version of the problem that includes an additional set (or layer) of nodes that are termed as physical nodes, such that a node in the social network is connected to one physical node. A physical node exists in one of two states at any time, opened or closed, and there is a constraint on the maximum number of physical nodes that can be opened. In this setting, an inactive node in the social network becomes active if it has at least one active neighbor in the social network and if it is connected to an opened physical node. This problem arises in scenarios such as disaster recovery, where a displaced social group (an inactive social node) decides to return back after a disaster (switches to active state) only after a sufficiently large number of groups in its social network return back and some infrastructure components (physical nodes) in its neighborhood are repaired (brought to the open state). We first show that this general problem is NP-hard to approximate within any constant factor. We then consider instances of the problem when the mapping between the social nodes and the physical nodes is bijective and characterize optimal and approximation algorithms for those instances.

Suggested Citation

  • Hemant Gehlot & Shreyas Sundaram & Satish V. Ukkusuri, 2023. "Algorithms for influence maximization in socio-physical networks," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-28, January.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:1:d:10.1007_s10878-022-00946-y
    DOI: 10.1007/s10878-022-00946-y
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    References listed on IDEAS

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    1. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions - 1," LIDAM Reprints CORE 334, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Zaixin Lu & Wei Zhang & Weili Wu & Joonmo Kim & Bin Fu, 2012. "The complexity of influence maximization problem in the deterministic linear threshold model," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 374-378, October.
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    4. Olivia Patterson & Frederick Weil & Kavita Patel, 2010. "The Role of Community in Disaster Response: Conceptual Models," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 29(2), pages 127-141, April.
    5. Ailian Wang & Weili Wu & Lei Cui, 2016. "On Bharathi–Kempe–Salek conjecture for influence maximization on arborescence," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1678-1684, May.
    6. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions," LIDAM Reprints CORE 341, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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