The complexity of point configurations

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Abstract

There are several natural ways to extend the notion of the order of points on a line to higher dimensions. This article focuses on three of them—combinatorial type, order type, and isotopy class—and surveys work done in recent years on the efficient encoding of order types and on complexity questions relating to all three classifications.

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Supported in part by NSF grant DMS-85-01492, NSA grant MDA904-89-H-2038, PSC-CUNY grant 666426, and the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS), a National Science Foundation Science and Technology Center, under NSF grant STC88-09648.

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Supported in part by NSF grants DMS-85-01947 and CCR-89-01484, NSA grant MDA904-89-H-2030, and DIMACS.