Abstract

We introduce and study a novel genre of optimization problems, which we call segmentation problems. Our motivation, in part, is the development of a framework for evaluating certain data mining and clustering operations in terms of their utility in decision-making. For any classical optimization problem, the corresponding segmentation problem seeks to partition a set of cost vectors into several segments, so that the overall cost is optimized. This framework contains a number of standard combinatorial clustering problems as special cases, and many segmentation problems turn out to be MAXSNP-complete even when the corresponding "un-segmented" version is easy to solve. We develop approximation algorithms for two natural and interesting problems in this class --- the HYPERCUBE SEGMENTATION PROBLEM and the CATALOG SEGMENTATION PROBLEM --- and present a general greedy scheme, which can be specialized to approximate a large class of segmentation problems. Finally, we indicate some connection...

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