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a b s t r a c tIn 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 k copies of each value in the degree sequence, this is a property proceeding from data privacy that is called k-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 k-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.

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.