1. Auburn University http://www.eng.auburn.edu/~xqin
COMP Advanced Computer and Network Security The VectorCover Algorithm (2)
Dr. Xiao Qin
Auburn University
Parking problem.
Go to office at 6:30 or 8:30 to bypass traffic jam
Spring, 2011

2. Minimal Distance Vectors
Note: show Fig. 4 (a) in the k-anonymity paper on the white board. Explain distance vector
Intuitively, the the minimal generalizations of table Ti are exactly those tables Tj satisfying k-anonymity with
minimal distance vectors DVi;j . For instance, with reference to the generalized tables illustrated in Figure 3 we
have already noticed how, for k = 3, GT[1;1] cannot be minimal because GT[0;1] and GT[1;0] also satisfy k-anonimity.

3. The Outlier Set and All Set
Outliers: Tuples which have less than k occurrences
All: a set of distinct tuples in a table

4. Pair – (strategy, tuples)
New data structure
Represents a transformation strategy
Represents a set of tuples after applying such a transformation.
Strategy = Distrance Vectors

5. Distance between Two Tuples

6. The VectorCover Algorithm
Draw (1) Fig. 3 table PT and (2) Fig. 4(a) on the white board

7. COMP 7370 Advanced Computer and Network Security The MinGen Algorithm
Dr. Xiao Qin
Auburn University
Parking problem.
Go to office at 6:30 or 8:30 to bypass traffic jam
Spring, 2011

9. Step 1: PT vs. PT[QI]
vs.

10. Step 2: history <- [d_1, … d_n]
Use subscripts to represent generalization strategies.
n =2
E_0 -> d_1 = 0
Z_0 -> d_2 = 0
Use subscripts to represent generalization strategies.
E_1 -> d_1 = ?
Z_2 -> d_2 = ?
E_1 -> d_1 = 1
Z_2 -> d_2 = 2

11. Step 2: history <- [d_1, … d_n]
Note: E_i and Z_j must be specific when you implement the MinGen algorithm.
You must specify your generalization strategies. For example:
Use subscripts to represent generalization strategies.

12. Step 2: E_i, Z_j n =2 E_0 -> d_1 = 0 Z_0 -> d_2 = 0
Use subscripts to represent generalization strategies.
E_1 -> d_1 = ?
Z_2 -> d_2 = ?
E_1 -> d_1 = 1
Z_2 -> d_2 = 2

13. Step 3: Check single attributes
Each single attribute must satisfy k-anonymity
E -> MGT[E]
v = a -> freq(a, MGT[E]) = ?
If 4 < k then what does this mean?
What should we do? 4

14. Step 3.1: Check single attributes
Each single attribute must satisfy k-anonymity 4
If 4 < k then we need data generalization!
V_E = [d_E, d_Z] = [1, 0] not [0, 1]
Note: move one step at a time.

15. Step 3.2: the generalize() function
Each single attribute must satisfy k-anonymity
E -> MGT[E]
Value v = a -> freq(a, MGT[E]) = ?
If 4 < k then what does this mean?
V_E = [d_E, d_Z] = [1, 0]
MGT <- generalize(MGT, V_E, [0,0]) 4

16. Step 3.2: the generalize() function
Each single attribute must satisfy k-anonymity
MGT <- generalize(MGT, v, h)
Generalize() transform MGT based on a generalization strategy specified by v, h.

17. Step 3.3: update the history vector
Each single attribute must satisfy k-anonymity
Can you give me an example to illustrate how step 3.3 works?
History [d_E, d_Z] = [0, 0]
V_E = [1, 0]
New History [0, 0] + [1, 0] = [1, 0]

18. Step 6.2

19. Step 6.3