k-Anonymity for object-orientated databases

Question

Based on this theoretical work of Latanya Sweeney about k-anonymity:

Definition 2.1 (Quasi-Identifier)

Let $T(A_1,...,A_n)$ be a table. A quasi-identifier of $T$ is a set of attributes $\{A_i,...,A_j\}\subseteq\{A_1,...,A_n\}$ whose release must be controlled.

Definition 2.2 (k-anonymity)

Let $T(A_1,...,A_n)$ be a table and $QT$ be the quasi-identifiers associated with it. $T$ is said to satisfy k-anonymity if for each quasi-identifier $$QI \in QT$:$ each sequence of values in $T[QI]$ appears at least with $k$ occurrences in $T[QI]$ .

Can anyone approve these next assumptions on an object-oriented approach?

Definition 1.1 (object-table)

Let $T(A_1,...,A_n)$ and $OT(OA_1,...,OA_n)$ be a table and $f_a:T\rightarrow OT$ a mapping from the original table $T$ to the object-table $OT$ .

Definition 1.2 (oject-space)

Let there be a space of all alterations $OT_i=\{\{OA_{1,1},...,OA_{1,n}\},...,\{OA_{m,1},...,OA_{m,n}\}\}$ of one object-attribute $OA_i$ and a space of functions $OF={f_{b,i}:OT\rightarrow OT_i}$ mapping between those.

Definition 1.2b

${OA_{1,1},...,OA_{1,n}}=OT$ and $f_{b,1}:OT\rightarrow&space;OT$ so $f_{b,1}$ is the non-anonymizing-function.

Definition 1.3 (quasi-identifier)

Let $QOT$ be a the qausi-identifier regarding the space $OA_i$ as $\{OA_{i,j}..OA_{k,l}\}\subseteq\{OA_{1,1}..OA_{m,n}\}$ with $\exists p_i \in U: f_a(f_c(p_i)[Q_OT])=p_i$

Definition 1.4

Let $ORT$ be a second table and $QOT$ be the quasi-identifiers associated with it. $ORT$ is said to satisfy k-anonymity if for each quasi-identifier $$QI \in QOT$:$ each sequence of values in $ORT[QI]$ appears at least with $k$ occurrences in .

So there is a bridge between the k-anonymity and the k-anonymity inbetween space of attributes and their anonymisations

k-Anonymity for object-orientated databases

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