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Hardness of Bounding Influence via Graph Modification

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SOFSEM 2023: Theory and Practice of Computer Science (SOFSEM 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13878))

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Abstract

We consider the problem of minimally modifying graphs and digraphs by way of exclusively deleting vertices, exclusively deleting edges, or exclusively adding new edges, with or without connectivity constraints for the resulting graph or digraph, to ensure that centrality-based influence scores of all vertices satisfy either a specified lowerbound \(\mathcal {A}\) or upperbound \(\mathcal {B}\). Here, we classify the hardness of exactly or approximately solving this problem for: (1) all vertex- and edge-deletion cases for betweenness, harmonic, degree, and in-degree centralities; (2) all vertex-deletion cases for eigenvector, Katz, and PageRank centralities; (3) all edge-deletion cases for eigenvector, Katz, and PageRank centralities under a connectivity or weak-connectivity constraint; and (4) a set of edge-addition cases for harmonic, degree, and in-degree centralities. We show that some of our results, in particular multiple results concerning betweenness, eigenvector, Katz, and PageRank centralities, hold for planar graphs and digraphs. Finally, under a variety of constraints, we establish that no polynomial time constant factor approximation algorithm can exist for computing the cardinality of a minimum set of vertices or minimum set of edges whose deletion ensures a lowerbound betweenness centrality score, or a lower- or upperbound eigenvector, Katz, or PageRank centrality score (unless \(P = NP\)).

Supported by JSPS Kakenhi grants {20K21827, 21H05052, 20H05967}.

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Authors and Affiliations

  1. Division of Medical Data Informatics, Human Genome Center, Institute of Medical Science, University of Tokyo, 4-6-1 Shirokanedai, Minato-ku, Tokyo, 108-8639, Japan

    Robert D. Barish & Tetsuo Shibuya

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  1. Robert D. Barish
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    Leszek Gąsieniec

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Barish, R.D., Shibuya, T. (2023). Hardness of Bounding Influence via Graph Modification. In: Gąsieniec, L. (eds) SOFSEM 2023: Theory and Practice of Computer Science. SOFSEM 2023. Lecture Notes in Computer Science, vol 13878. Springer, Cham. https://doi.org/10.1007/978-3-031-23101-8_9

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  • DOI: https://doi.org/10.1007/978-3-031-23101-8_9

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