Minimal Networks: A Review
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Publication:2977710
DOI10.1007/978-3-319-40673-2_4zbMath1359.05117OpenAlexW2513487133MaRDI QIDQ2977710
A. A. Tuzhilin, Alexandr O. Ivanov
Publication date: 19 April 2017
Published in: Advances in Dynamical Systems and Control (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-319-40673-2_4
Small world graphs, complex networks (graph-theoretic aspects) (05C82) Research exposition (monographs, survey articles) pertaining to combinatorics (05-02) Deterministic network models in operations research (90B10)
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Cites Work
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- Estimates of Steiner subratio and Steiner-Gromov ratio
- The length of an extremal network in a normed space: Maxwell formula
- One-dimensional minimal fillings with negative edge weights
- The additivity criterion for finite metric spaces and minimal fillings
- The Gromov-Hausdorff metric on the space of compact metric spaces is strictly intrinsic
- Realization of plane graphs as closed locally minimal nets on convex polyhedra
- Steiner ratio for hyperbolic surfaces.
- Locally minimal trees in \(n\)-normed spaces
- The Steiner ratio conjecture of Gilbert-Pollak may still be open
- Stabilization of locally minimal trees
- Filling Riemannian manifolds
- Steiner minimal trees for regular polygons
- A proof of the Gilbert-Pollak conjecture on the Steiner ratio
- Graham's problem on shortest networks for points on a circle
- Minimal binary trees with a regular boundary: The case of skeletons with five endpoints
- Classification of closed locally minimal networks on flat Klein bottles
- The Steiner ratio of several discrete metric spaces
- The Steiner ratio for manifolds.
- On the history of the Euclidean Steiner tree problem
- The Steiner ratio Gilbert-Pollak conjecture is still open
- The structure of minimal Steiner trees in the neighborhoods of the lunes of their edges
- Generalized Maxwell formula for the length of a minimal tree with a given topology
- Branched coverings and Steiner ratio
- One-dimensional Gromov minimal filling problem
- Closed locally minimal nets on tetrahedra
- On the Problem of Steiner
- Uniqueness of Steiner minimal trees on boundaries in general position
- Steiner Minimal Trees on Zig-Zag Lines
- Steiner Minimal Tree for Points on a Circle
- Steiner Minimal Trees on Chinese Checkerboards
- Minimal Mutation Trees of Sequences
- On Steiner Minimal Trees with Rectilinear Distance
- Steiner Trees for Ladders
- A.D. Alexandrov spaces with curvature bounded below
- CLASSIFICATION OF CLOSED MINIMAL NETWORKS ON FLAT TWO-DIMENSIONAL TORI
- Minimal binary trees with regular boundary: the case of sceletons with four ends
- The twist number of planar linear trees
- The local Steiner problem in normed planes
- Branching geodesics in normed spaces
- Steiner Trees on a Checkerboard
- CONVEX DOMAINS WITH NONCOMPACT AUTOMORPHISM GROUPS
- SOME PROBLEMS CONCERNING MINIMAL NETWORKS
- Distance matrix of a graph and its realizability
- A formula for the weight of a minimal filling of a finite metric space
- Steiner Minimal Trees
- A note on the tree realizability of a distance matrix
- Sets admitting connection by graphs of finite length
- Nontrivial critical networks. Singularities of Lagrangians and a criterion for criticality