Robotics Research Technical Report: Planar Realizations of Nonlinear Davenport-Schinzel Sequences by Segments (Classic Reprint) - Hardcover

Ady Wiernik

Hardcover

ISBN 10: 0332360024 ISBN 13: 9780332360027

Publisher: Forgotten Books, 2018

Synopsis

Explore how nonlinear Davenport–Schinzel sequences come to life as concrete planar segments.

This technical report presents an explicit method to realize complex sequences with simple geometric building blocks, turning abstract bounds into visible constructs. The work links sequence theory to practical planar arrangements, highlighting how lower envelopes of segments behave in the plane.

In clear steps, the authors take nonlinear DS(n,3) sequences and realize them with collections of line segments. The construction is designed to be explicit and analyzable, showing how intricate combinatorial limits translate into real geometric layouts. The result tightens understanding of the complexity of lower envelopes and related problems in computational geometry, with careful induction and rigorous reasoning.

• How DS(n,s) sequences describe the interactions of real-valued functions and their lower envelopes.
• An explicit, step-by-step method to realize nonlinear DS(n,3) sequences using planar segments.
• Why this realization helps bound the complexity of geometric problems and informs algorithm design.
• Connections between sequence theory and practical geometric constructions in the plane.

Ideal for readers of advanced computational geometry and researchers seeking concrete realizations from combinatorial bounds.

Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 0332360024
• ISBN 13: 9780332360027
• Binding: Hardcover
• Number of pages: 51