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Overview Study an important privacy preserving method, namely k-anonymity

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2D representation of the original and generalized table. Name. Age. Start-year. Salary. Alice. 25. 2001. 7k. Bob. 30. 2004. 1k. Christina. 35. 1990. 2k. Complexity and Approximation Ratio d : dimensionality n : the size of dataset. Daniel. 40. 1995. 3k. Emily.

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slide1

2D representation of the original and generalized table.

Name

Age

Start-year

Salary

Alice

25

2001

7k

Bob

30

2004

1k

Christina

35

1990

2k

Complexity and Approximation Ratio

d: dimensionality n: the size of dataset

Daniel

40

1995

3k

Emily

45

2000

6k

William

55

1985

3k

Algorithm

Time Complexity

Approximation Ratio

The original payroll table

DAG

O(3ddnlog2n)

8d

MMG

O(dn2d+1)

2d+1

Age

Start-year

Salary

NNG

O(dn2)

6d

[25, 45]

[2000, 2004]

7k

[25, 45]

[2000, 2004]

1k

[35, 55]

[1985, 1995]

2k

[35, 55]

[1985, 1995]

3k

[25, 45]

[2000, 2004]

6k

[35, 55]

[1985, 1995]

3k

A 3-anonymous generalization

The Institute for Information AssuranceOn Multidimensional k-Anonymity with Local Recoding GeneralizationPresented by: Yang DuCollege of Computer and Information ScienceNortheastern University, Boston, MA [email protected]

  • Overview
  • Study an important privacy preserving method, namely k-anonymity
  • Show it is provably hard, even to find a good enough approximate answer
  • Develop three algorithms with different tradeoffs between the approximation ratio and complexity
  • Introduction
  • Motivation is privacy preserving
    • Publish sensitive data to allow accurate analysis without revealing the privacy
  • Simply removing the id column is not enough
    • Attackers can use some other attributions, called quasi-identifiers, to restore the identities
  • Generalization is necessarily
    • The quasi-identifiers are replaced by values in more general forms
  • K-anonymity is often a requirement
    • Make the quasi-identifiers of each tuple undistinguishable with at least those of other (k-1) tuples
  • Approximation Algorithms
  • The Divide-and-Group (DAG) Algorithm
  • Divide the space into square cells with proper size
  • Find a set of non-overlapping tiles of 2 x 2 cells to cover the points, such that each tile covers at least k points
  • Assign the rest of (uncovered) points to the nearest tile
  • Problem Mapping
  • Given a table R containing d quasi-identifier attributes
  • Map each quasi-identifier attribute to one dimension
  • Map each tuple in the table to a point in d-dimensional space
  • Map the k-anonymous generalization problem to a partition problem
    • Partition a set of d-dimensional points into some groups
    • Each point belongs to one and only one group
    • Each group contains at least k points
    • Each point is generalized to the minimum bounding rectangle (MBR) of its group
  • Quality Measuring
  • The smaller the MBRs are, the more accurate the analysis results are.
  • The size of each MBR is measured by its perimeter.
  • Objective
    • Find the optimal partition that minimizes the maximum size (perimeter) among all MBRs.
  • The Min-MBR-Group (MMG) Algorithm
  • For each point p, find the smallest MBR which covers at least k points including p
  • Find a set of non-overlapping MBRs from the result of previous step
  • Assign the points to the nearest MBR
  • The Nearest-MBR-Group (NNG) Algorithm
  • For each point p, find the MBR which covers p and its k-1 nearest neighbors
  • Find a set of non-overlapping MBRs from the result of previous step
  • Assign the points to the nearest MBR
  • Hardness of the Problem
  • Finding the optimal partition is NP-hard (cannot be done within polynomial time).
  • Finding a partition with approximation ratio less than 5/4, i.e. the maximum perimeter is 5/4 of the maximum perimeter of the optimal partition, is also NP-hard.
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