The complexity of degree anonymization by vertex addition

Motivated by applications in privacy-preserving data publishing, we study the problem of making an undirected graph k-anonymous by adding few vertices (together with some incident edges). That is, after adding these “dummy vertices”, for every vertex degree d appearing in the resulting graph, there...

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Bibliographic Details
Published in:Theoretical computer science Vol. 607; pp. 16 - 34
Main Authors: Bredereck, Robert, Froese, Vincent, Hartung, Sepp, Nichterlein, André, Niedermeier, Rolf, Talmon, Nimrod
Format: Journal Article
Language:English
Published: Elsevier B.V 23.11.2015
Subjects:
Complexity
Computation
Degree-constrained editing
Dummies
Fixed-parameter tractability
Graph modification
Graph theory
Graphs
Kernelization
NP-hardness
Parameterized complexity
Trees
NP-hardness
Degree-constrained editing
Graph modification
Fixed-parameter tractability
Parameterized complexity
Kernelization
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:Motivated by applications in privacy-preserving data publishing, we study the problem of making an undirected graph k-anonymous by adding few vertices (together with some incident edges). That is, after adding these “dummy vertices”, for every vertex degree d appearing in the resulting graph, there shall be at least k vertices with degree d. We explore three variants of vertex addition (justified by real-world considerations) and study their (parameterized) computational complexity. We derive mostly intractability results, even for very restricted cases (including trees and bounded-degree graphs) but also obtain some encouraging fixed-parameter tractability results. •Degree anonymization by vertex addition is computationally intractable in general.•Posing structural restrictions on the edges connected to the new vertices seems to make the problem even harder.•There are some tractable special cases, for example, when the number of new edges is small.
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2015.07.004