A variational approach to the Steiner network problem

DOI10.1007/BF02071984zbMath0734.05040OpenAlexW2075207773WikidataQ61714645 ScholiaQ61714645MaRDI QIDQ810521

Doreen Anne Thomas, Joachim Hyam Rubinstein

Publication date: 1991

Published in: Annals of Operations Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02071984

zbMATH Keywords

minimal spanning treeGraham's problemshortest Steiner networkSteiner ratio conjecture

Mathematics Subject Classification ID

Programming involving graphs or networks (90C35) Trees (05C05)

Related Items (24)

Symmetrization theorem of full Steiner trees ⋮ Some results on greedy algorithm conjectures ⋮ Variational approach and Steiner minimal trees on four points ⋮ On greedy heuristic for Steiner minimum trees ⋮ Optimum steiner ratio for gradient-constrained networks connecting three points in 3-space, part II: The gradient-constraint m satisfies \documentclass{article} \usepackage{amsmath,amsfonts,amssymb}\pagestyle{empty}\begin{document}$ 1 \leq m \leq \sqrt{3} ⋮ Full minimal Steiner trees on lattice sets ⋮ Upper and lower bounds for the lengths of Steiner trees in 3-space ⋮ Determining shortest networks in the Euclidean plane ⋮ Non-crossing of plane minimal spanning and minimal T1 networks ⋮ Minimum Steiner trees on a set of concyclic points and their center ⋮ Analytic deformations of minimal networks ⋮ Computing Steiner points for gradient-constrained minimum networks ⋮ Euclidean Steiner trees optimal with respect to swapping 4-point subtrees ⋮ The Steiner ratio conjecture for six points ⋮ A primer of the Euclidean Steiner problem ⋮ Directional derivative of the weight of a minimal filling in Riemannian manifolds ⋮ The Steiner ratio conjecture for cocircular points ⋮ Graham's problem on shortest networks for points on a circle ⋮ Minimal curvature-constrained networks ⋮ The Steiner minimal network for convex configurations ⋮ Optimum Steiner ratio for gradient‐constrained networks connecting three points in 3‐space, part I ⋮ The Steiner problem on surfaces of revolution ⋮ Gradient-constrained minimum networks. II: Labelled or locally minimal Steiner points ⋮ IDENTIFYING STEINER MINIMAL TREES ON FOUR POINTS IN SPACE

Cites Work

• On the shortest spanning subtree of a graph and the traveling salesman problem
• The Steiner ratio conjecture is true for five points
• Topology of three dimensional manifolds and the embedding problems in minimal surface theory
• Curvature, diameter and Betti numbers
• The Steiner ratio conjecture for six points
• The Steiner ratio conjecture for cocircular points
• Some remarks on the Steiner problem
• A short proof of a result of Pollak on Steiner minimal trees
• On the Problem of Steiner
• The Complexity of Computing Steiner Minimal Trees
• Steiner Minimal Trees

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