Approximation Algorithms for Min-Max Generalization Problems

Piotr Berman, Sofya Raskhodnikova

Abstract: 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 lb, and the goal is to partition individual items into groups of weight at least w lb, 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.