On the Steiner ratio in 3-space

DOI10.1016/0097-3165(95)90055-1zbMath0831.05021OpenAlexW2073692857MaRDI QIDQ1345879

Warren D. Smith, James MacGregor Smith

Publication date: 12 February 1996

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0097-3165(95)90055-1

zbMATH Keywords

minimum spanning treeSteiner minimal treepoint setSteiner ratio\(d\)-sausage

Mathematics Subject Classification ID

Trees (05C05) Extremal problems in graph theory (05C35) Distance in graphs (05C12)

Related Items

A new heuristic for the Euclidean Steiner tree problem in \(\mathbb{R}^n\), Minimal spanning trees on infinite sets, Euclidean Steiner minimal trees, minimum energy configurations, and the embedding problem of weighted graphs in \(E^ 3\), A sausage heuristic for Steiner minimal trees in three-dimensional Euclidean space

Uses Software

• FindSteinerTree

Cites Work

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• The Steiner problem with edge lengths 1 and 2
• Euclidean minimum spanning trees and bichromatic closest pairs
• How to find Steiner minimal trees in Euclidean \(d\)-space
• Graham's problem on shortest networks for points on a circle
• Improved computation of plane Steiner minimal trees
• Steiner minimal trees for a class of zigzag lines
• A heuristic for Euclidean and rectilinear Steiner problems
• Disproofs of generalized Gilbert-Pollak conjecture on the Steiner ratio in three or more dimensions
• On the Problem of Steiner
• Steiner Minimal Trees on Zig-Zag Lines
• Steiner problem in networks: A survey
• Minimum Spanning Trees in k-Dimensional Space
• An O(n logn) heuristic for steiner minimal tree problems on the euclidean metric
• Finding Minimum Spanning Trees
• A Lower Bound for the Steiner Tree Problem
• Steiner Trees for Ladders
• The Complexity of Computing Steiner Minimal Trees
• Steiner Trees on a Checkerboard
• An efficient method for finding the minimum of a function of several variables without calculating derivatives
• Steiner Minimal Trees
• Euclidean Constructibility in Graph-Minimization Problems
• The Generation of Minimal Trees with a Steiner Topology
• The Closest Packing of Spherical Caps in n Dimensions
• Steiner tree problems