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On the Complexity of k-Metric Antidimension Problem and the Size of k-Antiresolving Sets in Random Graphs

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Computing and Combinatorics (COCOON 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10392))

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Abstract

Network analysis has benefited greatly from published data of social networks. However, the privacy of users may be compromised even if the data are released after applying anonymization techniques. To measure the resistance against privacy attacks in an anonymous network, Trujillo-Rasua R. et al. introduce the concepts of k-antiresolving set and k-metric antidimension [1]. In this paper, we prove that the problem of k-metric antidimension is NP-hard. We also study the size of k-antiresolving sets in random graphs. Specifically, we establish three bounds on the size of k-antiresolving sets in Erdős-Rényi random graphs.

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Notes

  1. 1.

    After finishing our proof, we found that Chatterjee T. et al. had proved that the problem of computing adim\(_k(G)\) is NP-hard by a different reduction independently [10].

  2. 2.

    X3C is a well known NP-complete problem [13].

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Authors and Affiliations

  1. Department of Computer Science, University of British Columbia Okanagan, Kelowna, BC, V1V 1V7, Canada

    Congsong Zhang & Yong Gao

Authors
  1. Congsong Zhang
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  2. Yong Gao
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Correspondence to Congsong Zhang .

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Editors and Affiliations

  1. Department of Computing, Hong Kong Polytechnic University, Hong Kong, China

    Yixin Cao

  2. Texas A&M University, College Station, Texas, USA

    Jianer Chen

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Zhang, C., Gao, Y. (2017). On the Complexity of k-Metric Antidimension Problem and the Size of k-Antiresolving Sets in Random Graphs. In: Cao, Y., Chen, J. (eds) Computing and Combinatorics. COCOON 2017. Lecture Notes in Computer Science(), vol 10392. Springer, Cham. https://doi.org/10.1007/978-3-319-62389-4_46

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  • DOI: https://doi.org/10.1007/978-3-319-62389-4_46

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62388-7

  • Online ISBN: 978-3-319-62389-4

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