Improving the characterization of P-stability for applications in network privacy

Salas, Julián; Torra, Vicenç

doi:10.1016/j.dam.2016.01.025

Cited by 13 publications

(8 citation statements)

References 24 publications

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“…, d n ) with (i) δ(d) ≥ 1 and ∆(d) ≤ 2 √ n − 2, or (ii) δ(d) ≥ 1 4 n and ∆(d) ≤ 3 4 n − 1 satisfy (3) but not necessarily the conditions in [25]. We refer the reader to [27,38] for more examples. The bounds in Corollaries 5 and 6 are in a sense best possible with respect to the graph parameters involved.…”

Section: Sampling Undirected Graphsmentioning

confidence: 99%

Rapid Mixing of the Switch Markov Chain for Strongly Stable Degree Sequences and 2-Class Joint Degree Matrices

Amanatidis¹,

Kleer²

2019

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

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The switch Markov chain has been extensively studied as the most natural Markov Chain Monte Carlo approach for sampling graphs with prescribed degree sequences. We use comparison arguments with other-less natural but simpler to analyze-Markov chains, to show that the switch chain mixes rapidly in two different settings. We first study the classic problem of uniformly sampling simple undirected, as well as bipartite, graphs with a given degree sequence. We apply an embedding argument, involving a Markov chain defined by Jerrum and Sinclair (TCS, 1990) for sampling graphs that almost have a given degree sequence, to show rapid mixing for degree sequences satisfying strong stability, a notion closely related to P-stability. This results in a much shorter proof that unifies the currently known rapid mixing results of the switch chain and extends them up to sharp characterizations of P-stability. In particular, our work resolves an open problem posed by Greenhill (SODA, 2015).Secondly, in order to illustrate the power of our approach, we study the problem of uniformly sampling graphs for which-in addition to the degree sequence-a joint degree distribution is given. Although the problem was formalized over a decade ago, and despite its practical significance in generating synthetic network topologies, small progress has been made on the random sampling of such graphs. The case of a single degree class reduces to sampling of regular graphs, but beyond this almost nothing is known. We fully resolve the case of two degree classes, by showing that the switch Markov chain is always rapidly mixing. Again, we first analyze an auxiliary chain for strongly stable instances on an augmented state space and then use an embedding argument.

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Section: Sampling Undirected Graphsmentioning

confidence: 99%

Rapid Mixing of the Switch Markov Chain for Strongly Stable Degree Sequences and 2-Class Joint Degree Matrices

Amanatidis¹,

Kleer²

2019

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…In [32] and [33] this is used to prove that scale-free sequences with parameter γ > 2 are P-stable and graphic. Note that the P-stability property guarantees that a graph with a given degree sequence may be uniformly generated by choosing a graph G ∈ D(n, d n ) by applying sufficient random swaps.…”

Section: Degree Preserving Randomizationmentioning

confidence: 99%

Graph Perturbation as Noise Graph Addition: A New Perspective for Graph Anonymization

Torra

Salas

2019

Lecture Notes in Computer Science

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Different types of data privacy techniques have been applied to graphs and social networks. They have been used under different assumptions on intruders' knowledge. i.e., different assumptions on what can lead to disclosure. The analysis of different methods is also led by how data protection techniques influence the analysis of the data. i.e., information loss or data utility. One of the techniques proposed for graph is graph perturbation. Several algorithms have been proposed for this purpose. They proceed adding or removing edges, although some also consider adding and removing nodes. In this paper we propose the study of these graph perturbation techniques from a different perspective. Following the model of standard database perturbation as noise addition, we propose to study graph perturbation as noise graph addition. We think that changing the perspective of graph sanitization in this direction will permit to study the properties of perturbed graphs in a more systematic way.

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“…Graph modifications to guarantee k-degree anonymity have additional restrictions, for example, the k-anonymous degree sequences must be graphic, i.e., they must correspond to the sequence of degrees of a graph. Some theoretical conditions for degree sequences to be graphic and applications to k-degree anonymization and edge randomization can be found in [8,9].…”

Section: Introductionmentioning

confidence: 99%

A General Algorithm for k-anonymity on Dynamic Databases

Salas

Torra

2018

Lecture Notes in Computer Science

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In this work we present an algorithm for k-anonymization of datasets that are changing over time. It is intended for preventing identity disclosure in dynamic datasets via microaggregation. It supports adding, deleting and updating records in a database, while keeping k-anonymity on each release.We carry out experiments on database anonymization. We expected that the additional constraints for k-anonymization of dynamic databases would entail a larger information loss, however it stays close to MDAV's information loss for static databases.Finally, we carry out a proof of concept experiment with directed degree sequence anonymization, in which the removal or addition of records, implies the modification of other records.

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Improving the characterization of P-stability for applications in network privacy

Cited by 13 publications

References 24 publications

Rapid Mixing of the Switch Markov Chain for Strongly Stable Degree Sequences and 2-Class Joint Degree Matrices

Rapid Mixing of the Switch Markov Chain for Strongly Stable Degree Sequences and 2-Class Joint Degree Matrices

Graph Perturbation as Noise Graph Addition: A New Perspective for Graph Anonymization

A General Algorithm for k-anonymity on Dynamic Databases

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