On the Approximability of Geometric and Geographic Generalization and the Min-Max Bin Covering Problem

TL;DR

This paper investigates the limits of approximating data generalization for privacy, proving hardness results and providing algorithms that perform near optimal, with a novel connection to the min-max bin covering problem.

Contribution

It establishes the computational hardness of approximating certain data generalization problems and introduces approximation algorithms, linking the problem to a new bin packing variant.

Findings

Hardness results for approximating generalization with geographic or unordered attributes

Approximation algorithms that perform close to optimal in practice

Introduction of the min-max bin covering problem as a new related challenge

Abstract

We study the problem of abstracting a table of data about individuals so that no selection query can identify fewer than k individuals. We show that it is impossible to achieve arbitrarily good polynomial-time approximations for a number of natural variations of the generalization technique, unless P = NP, even when the table has only a single quasi-identifying attribute that represents a geographic or unordered attribute: Zip-codes: nodes of a planar graph generalized into connected subgraphs GPS coordinates: points in R2 generalized into non-overlapping rectangles Unordered data: text labels that can be grouped arbitrarily. In addition to impossibility results, we provide approximation algorithms for these difficult single-attribute generalization problems, which, of course, apply to multiple-attribute instances with one that is quasi-identifying. We show theoretically and experimentally that our approximation algorithms can come reasonably close to optimal solutions. Incidentally, the generalization problem for unordered data can be viewed as a novel type of bin packing problem--min-max bin covering--which may be of independent interest.