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Finding groups with maximum betweenness centrality via integer programming with random path sampling

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Abstract

One popular approach to access the importance/influence of a group of nodes in a network is based on the notion of centrality. For a given group, its group betweenness centrality is computed, first, by evaluating a ratio of shortest paths between each node pair in a network that are “covered” by at least one node in the considered group, and then summing all these ratios for all node pairs. In this paper we study the problem of finding the most influential (or central) group of nodes (of some predefined size) in a network based on the concept of betweenness centrality. One known approach to solve this problem exactly relies on using a linear mixed-integer programming (linear MIP) model. However, the size of this MIP model (with respect to the number of variables and constraints) is exponential in the worst case as it requires computing all (or almost all) shortest paths in the network. We address this limitation by considering randomized approaches that solve a single linear MIP (or a series of linear MIPs) of a much smaller size(s) by sampling a sufficiently large number of shortest paths. Some probabilistic estimates of the solution quality provided by our approaches are also discussed. Finally, we illustrate the performance of our methods in a computational study.

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Notes

  1. A multiset is a generalization of a set and allows multiple instances of each of its elements.

  2. The additional datasets generated during and/or analysed during the current study are available from the corresponding author on request.

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Acknowledgements

The authors are grateful to Dr. Oliver Hinder for pointing out an issue in the early version of the paper as well as his subsequent comments. Also, we would like to thank the anonymous referees for the comments and suggestions, which helped us to improve the paper.

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Authors and Affiliations

  1. Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA, 15261, USA

    Tomás Lagos & Oleg A. Prokopyev

  2. Department of Industrial Engineering and Management Systems, University of Central Florida, Orlando, FL, 32816, USA

    Alexander Veremyev

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  1. Tomás Lagos
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  2. Oleg A. Prokopyev
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  3. Alexander Veremyev
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Correspondence to Oleg A. Prokopyev.

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This research was partially supported by NSF grants CBET-1803527 and CMMI-2002681.

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Lagos, T., Prokopyev, O.A. & Veremyev, A. Finding groups with maximum betweenness centrality via integer programming with random path sampling. J Glob Optim 88, 199–232 (2024). https://doi.org/10.1007/s10898-022-01269-2

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  • DOI: https://doi.org/10.1007/s10898-022-01269-2

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