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  • 1.
    Salas, Julian
    et al.
    Department of Computer Engineering and Mathematics, Universitat Rovira i Virgili, Tarragona, Spain.
    Torra, Vicenç
    Högskolan i Skövde, Institutionen för informationsteknologi. Högskolan i Skövde, Forskningscentrum för Informationsteknologi.
    Improving the characterization of P-stability for applications in network privacy2016Inngår i: Discrete Applied Mathematics, ISSN 0166-218X, E-ISSN 1872-6771, Vol. 206, s. 109-114Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Recently, we have found that the concept of P-stability has interesting applications in network privacy. In the context of Online Social Networks it may be used for obtaining a fully polynomial randomized approximation scheme for graph masking and measuring disclosure risk. Also by using the characterization for P-stable sequences from Jerrum, McKay and Sinclair (1992) it is possible to obtain optimal approximations for the problem of k-degree anonymity. In this paper, we present results on P-stability considering the additional restriction that the degree sequence must not intersect the edges of an excluded graph X, improving earlier results on P-stability. As a consequence we extend the P-stable classes of scale-free networks from Torra et al. (2015), obtain an optimal solution for k-anonymity and prove that all the known conditions for P-stability are sufficient for sequences to be graphic. (C) 2016 Elsevier B.V. All rights reserved.

  • 2.
    Salas, Julián
    et al.
    IIIA-CSIC, Consejo Superior de Investigaciones Científicas, Institut d’Investigació en Intelligència Artificial, Campus Universitat Autònoma de Barcelona, Spain.
    Torra, Vicenç
    Högskolan i Skövde, Institutionen för informationsteknologi. Högskolan i Skövde, Forskningscentrum för Informationsteknologi. IIIA-CSIC, Consejo Superior de Investigaciones Científicas, Institut d’Investigació en Intelligència Artificial, Campus Universitat Autònoma de Barcelona, Spain.
    Graphic sequences, distances and k-degree anonymity2015Inngår i: Discrete Applied Mathematics, ISSN 0166-218X, E-ISSN 1872-6771, Vol. 188, nr 1, s. 25-31Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we study conditions to approximate a given graph by a regular one. We obtain optimal conditions for a few metrics such as the edge rotation distance for graphs, the rectilinear and the Euclidean distance over degree sequences. Then, we require the approximation to have at least kk copies of each value in the degree sequence, this is a property proceeding from data privacy that is called kk-degree anonymity.

    We give a sufficient condition in order for a degree sequence to be graphic that depends only on its length and its maximum and minimum degrees. Using this condition we give an optimal solution of kk-degree anonymity for the Euclidean distance when the sum of the degrees in the anonymized degree sequence is even. We present algorithms that may be used for obtaining all the mentioned anonymizations.

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