Robotics Research Technical Report, Vol. 255: The Complexity of Many Faces in Arrangements of Lines and of Segments (Classic Reprint) - Hardcover

Herbert Edelsbrunner

Hardcover

ISBN 10: 0267851022 ISBN 13: 9780267851027

Publisher: Forgotten Books, 2018

Synopsis

Discover how many faces can appear in arrangements of lines and line segments, and how to compute them efficiently.

This book presents tight upper bounds on the complexity of faces in planar line arrangements and shows practical ways to construct these faces with fast, randomized algorithms. It uses new ideas like a partition tree and specialized combination lemmas to analyze how faces merge and interact in recursive layouts.

• Provides almost tight bounds on the maximum number of edges bounding m faces in an arrangement of n lines or line segments.
• Introduces a partitioning approach and randomized techniques to manage points and lines efficiently.
• Describes algorithms to construct faces, with running times close to the size of the output.
• Extends classical results to line segments, offering a broader view of combinatorial geometry in the plane.

Ideal for readers of computational geometry, algorithm design, and researchers exploring planar arrangements and their applications.

Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 0267851022
• ISBN 13: 9780267851027
• Binding: Hardcover
• Number of pages: 44