External-Memory Computational Geometry

(c) 1993 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper we give new techniques for designing e cient algorithms for computational geometry prob- lems that are too large to be solved in internal mem- ory. We use these techniques to develop optimal and practical algorithms for a number of important large- scale problems. We discuss our algorithms primarily in the context of single processor/single disk machines, a domain in which they are not only the rst known optimal results but also of tremendous practical value. Our methods also produce the rst known optimal al- gorithms for a wide range of two-level and hierarchical multilevel memory models, including parallel models. The algorithms are optimal both in terms of I/O cost and internal computation