Minimal NetworksThe Steiner Problem and Its Generalizations: 1st Edition (Hardback) book cover

Minimal NetworksThe Steiner Problem and Its Generalizations

1st Edition

By Alexander O. Ivanov, Alexei A. Tuzhilin

CRC Press

432 pages

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Hardback: 9780849386428
pub: 1994-03-16
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Description

This book focuses on the classic Steiner Problem and illustrates how results of the problem's development have generated the Theory of Minimal Networks, that is systems of "rubber" branching threads of minimal length. This theory demonstrates a brilliant interconnection among differential and computational geometry, topology, variational calculus, and graph theory. All necessary preliminary information is included, and the book's simplified format and nearly 150 illustrations and tables will help readers develop a concrete understanding of the material. All nontrivial statements are proved, and plenty of exercises are included.

Table of Contents

Some Necessary Results from Graph Theory and Geometry. The Steiner Problem and Its Modifications. Local Structure of Minimal Networks. Global Structure of Minimal Networks. Global Minimal Networks on the Plane. Planar Local Minimal Networks with Convex Boundaries. Planar Local Minimal Networks with Regular Boundaries. Closed Minimal Networks on Closed Surfaces of Constant Curvature. Minimal Networks in Other Spaces.

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT022000
MATHEMATICS / Number Theory
TEC009070
TECHNOLOGY & ENGINEERING / Mechanical