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A Refined Complexity Analysis of Degree Anonymization in Graphs
 IN PROCEEDINGS OF THE 40TH INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP ’13), LNCS
, 2013
"... Motivated by a strongly growing interest in graph anonymization in the data mining and databases communities over the last five years, we study the NPhard problem of making a graph kanonymous by adding as few edges as possible. Herein, a graph is kanonymous if for every vertex in the graph there ..."
Abstract

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Motivated by a strongly growing interest in graph anonymization in the data mining and databases communities over the last five years, we study the NPhard problem of making a graph kanonymous by adding as few edges as possible. Herein, a graph is kanonymous if for every vertex in the graph there are at least k − 1 other vertices of the same degree. Our algorithmic results shed light on the performance quality of a popular heuristic due to Liu and Terzi [ACM SIGMOD 2008]; in particular, we show that the heuristic provides optimal solutions in case that many edges need to be added. Based on this, we develop a polynomialtime data reduction, yielding a polynomialsize problem kernel for the problem parameterized by the maximum vertex degree. This result is in a sense tight since we also show that the problem is already NPhard for Hindex three, implying NPhardness for smaller parameters such as average degree and degeneracy.