Approximation Algorithms for Min-Max Generalization Problems

We provide improved approximation algorithms for the min-max 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 w(1b), and the goal is to partition individual items into groups of weight at least w(1b), 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: (I) 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.