Locating Lines and Hyperplanes

1. Front Matter

   Pages i-xi

   PDF

2. Basic Concepts

   • Anita Schöbel

   Pages 1-31

3. Line Location with Vertical Distance

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   Pages 33-46

4. Locating Lines in the Normed Plane

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   Pages 47-75

5. Finding All Optimal Lines

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   Pages 77-94

6. Line Location with Other Distances

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   Pages 95-113

7. Restricted Line Location Problems

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   Pages 115-138

8. Locating Hyperplanes in Normed Spaces

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   Pages 139-160

9. Extensions: Locating Other Objects

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   Pages 161-180

10. Back Matter

    Pages 181-200

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Line and hyperplane location problems play an important role not only in operations research and location theory, but also in computational geometry and robust statistics. This book provides a survey on line and hyperplane location combining analytical and geometrical methods. The major portion of the text presents new results on this topic, including the extension of some special cases to all distances derived from norms and a discussion of restricted problems in the plane. Almost all results are proven in the text and most of them are illustrated by examples. Furthermore, relations to classical facility location and to problems in computational geometry are pointed out.
Audience: The book is suitable for researchers, lecturers, and graduate students working in the fields of location theory or computational geometry.

• algorithms
• computational geometry
• geometry
• operations research
• statistics
• matrix theory

• Universität Kaiserslautern, Kaiserslautern, Germany

  Anita Schöbel

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