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**1 - 2**of**2**### Approximation Algorithms for Min-Max Generalization Problems

"... We provide improved approximation algorithms for the minmax generalization problems considered by Du, Eppstein, Goodrich, and Lueker [1]. In min-max generalization problems, the input consists of data items with weights and a lower bound wlb, and the goal is to partition individual items into grou ..."

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We provide improved approximation algorithms for the minmax generalization problems considered by Du, Eppstein, Goodrich, and Lueker [1]. In min-max generalization problems, the input consists of data items with weights and a lower bound wlb, and the goal is to partition individual items into groups of weight at least wlb, while minimizing the maximum weight of a group. The rules of legal partitioning are specific to a problem. Du et al. consider several problems in this vein: (1) partitioning a graph into connected subgraphs, (2) partitioning unstructured data into arbitrary classes and (3) partitioning a 2-dimensional array into non-overlapping contiguous rectangles (subarrays) that satisfy the above size requirements. We significantly improve approximation ratios for all the problems considered by Du et al., and provide additional motivation for these problems. Moreover, for the first problem, while Du et al. give approximation algorithms for specific graph families, namely, 3-connected and 4-connected planar graphs, no approximation algorithm that works for all graphs was known prior to this work.

### Parameterized Complexity of k-Anonymity: Hardness and Tractability

, 2010

"... The problem of publishing personal data without giving up privacy is becoming increasingly important. A clean formalization that has been recently proposed is the k-anonymity, where the rows of a table are partitioned in clusters of size at least k and all rows in a cluster become the same tuple, af ..."

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The problem of publishing personal data without giving up privacy is becoming increasingly important. A clean formalization that has been recently proposed is the k-anonymity, where the rows of a table are partitioned in clusters of size at least k and all rows in a cluster become the same tuple, after the suppression of some entries. The natural optimization problem, where the goal is to minimize the number of suppressed entries, is hard even when the stored values are over a binary alphabet and as well as on a table consists of a bounded number of columns. In this paper we study how the complexity of the problem is influenced by different parameters. First we show that the problem is W[1]-hard when parameterized by the value of the solution (and k). Then we exhibit a fixed-parameter algorithm when the problem is parameterized by the number of columns and the maximum number of different values in any column. Finally, we prove that k-anonymity is still APX-hard even when restricting to instances with 3 columns and k = 3. 1