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An Atlas of Steiner Networks
Arlinghaus, Sandra Lach; Arlinghaus, S. L.
1989
Citation:Arlinghaus, Sandra Lach. An Atlas of Steiner Networks. Ann Arbor: Institute of Mathematical Geography, Monograph Series, Monograph #9, 1989. 89 pages. http://hdl.handle.net/2027.42/58268
Abstract: Table of Contents: Introduction | Networks of Minimal Total Length in the Triangle | Networks of Minimal Total Length, in General | Geometric Constructions: the Six Point Case | Enumeration of Candidate Steiner Networks
Series/Report no.:Institute of Mathematical Geography (IMaGe) Monograph Series., Monograph #9.
Subject(s):Steiner networks, shortest paths
Description: A Steiner network is a tree of minimum total length joining a prescribed, finite, number of locations; often new locations are introduced into the prescribed set to determine the minimum tree. This Atlas explains the mathematical detail behind the Seiner construction for prescribed sets of n locations and displays the steps, visually, in a series of Figures. The proof of the STeiner construction is by mathematical induction, and enough steps in the early part of the induction are displayed, completely that the reader who is well-trained in Euclidean geometry, and familiar with concepts from graph theory and elementary number theory,, should be able to replicate the constructions for full as well as for degenerate Steiner trees.
