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There are planar graphs almost as good as the complete graphs and almost as cheap as minimum spanning trees

https://doi.org/10.1007/bf01758846
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/3-540-19487-8_23openalex-snapshot
Approximating the complete Euclidean graph
inferredcites →https://doi.org/10.1007/3-540-51542-9_6openalex-snapshot
The Delaunay triangulation closely approximates the complete Euclidean graph
inferredcites →https://doi.org/10.1007/3-540-51859-2_15openalex-snapshot
Which triangulations approximate the complete graph?
inferredcites →https://doi.org/10.1016/0020-0190(80)90062-9openalex-snapshot
A note on Delaunay and optimal triangulations
inferredcites →https://doi.org/10.1038/scientificamerican0189-84openalex-snapshot
The Shortest-Network Problem
inferredcites →https://doi.org/10.1109/sfcs.1987.18openalex-snapshot
Delaunay graphs are almost as good as complete graphs
inferredcites →https://doi.org/10.1137/0205051openalex-snapshot
Finding Minimum Spanning Trees
inferredcites →https://doi.org/10.1145/10515.10534openalex-snapshot
There is a planar graph almost as good as the complete graph

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1007/11602613_7openalex-snapshot
Sparse Geometric Graphs with Small Dilation
inferred← citeshttps://doi.org/10.1007/3-540-45071-8_38openalex-snapshot
Efficient Construction of Low Weight Bounded Degree Planar Spanner
inferred← citeshttps://doi.org/10.1007/3-540-45749-6_24openalex-snapshot
Constructing Plane Spanners of Bounded Degree and Low Weight
inferred← citeshttps://doi.org/10.1007/978-0-387-30162-4_167openalex-snapshot
Geometric Spanners
inferred← citeshttps://doi.org/10.1007/978-0-387-30162-4_294openalex-snapshot
Planar Geometric Spanners
inferred← citeshttps://doi.org/10.1007/978-1-4939-2864-4_294openalex-snapshot
Planar Geometric Spanners
inferred← citeshttps://doi.org/10.1007/978-3-319-29221-2_12openalex-snapshot
Lower Bounds on the Dilation of Plane Spanners
inferred← citeshttps://doi.org/10.1007/978-3-319-29221-2_13openalex-snapshot
Lattice Spanners of Low Degree
inferred← citeshttps://doi.org/10.1007/978-3-540-70918-3_16openalex-snapshot
Light Orthogonal Networks with Constant Geometric Dilation
inferred← citeshttps://doi.org/10.1007/978-3-540-87779-0_25openalex-snapshot
Computing Lightweight Spanners Locally
inferred← citeshttps://doi.org/10.1007/978-3-642-02017-9_8openalex-snapshot
On Spanners of Geometric Graphs
inferred← citeshttps://doi.org/10.1007/978-3-642-02085-8_23openalex-snapshot
Local Construction of Spanners in the 3-D Space
inferred← citeshttps://doi.org/10.1007/978-3-642-31594-7_25openalex-snapshot
Label Cover Instances with Large Girth and the Hardness of Approximating Basic k-Spanner
inferred← citeshttps://doi.org/10.1007/978-3-642-31770-5_20openalex-snapshot
On Certain Geometric Properties of the Yao-Yao Graphs
inferred← citeshttps://doi.org/10.1007/bf01294129openalex-snapshot
Balancing minimum spanning trees and shortest-path trees
inferred← citeshttps://doi.org/10.1007/s00453-005-1168-8openalex-snapshot
Constructing Plane Spanners of Bounded Degree and Low Weight
inferred← citeshttps://doi.org/10.1007/s00453-009-9329-9openalex-snapshot
Minimum Weight Convex Steiner Partitions
inferred← citeshttps://doi.org/10.1007/s00453-022-00930-2openalex-snapshot
Local Routing in Sparse and Lightweight Geometric Graphs
inferred← citeshttps://doi.org/10.1007/s00454-004-1121-7openalex-snapshot
Fault-Tolerant Geometric Spanners
inferred← citeshttps://doi.org/10.1007/s10878-012-9570-zopenalex-snapshot
On certain geometric properties of the Yao–Yao graphs
inferred← citeshttps://doi.org/10.1016/j.comgeo.2007.07.004openalex-snapshot
Sparse geometric graphs with small dilation
inferred← citeshttps://doi.org/10.1016/j.comgeo.2007.12.001openalex-snapshot
Computing a minimum-dilation spanning tree is NP-hard
inferred← citeshttps://doi.org/10.1016/j.comgeo.2013.04.002openalex-snapshot
On plane geometric spanners: A survey and open problems
inferred← citeshttps://doi.org/10.1016/j.comgeo.2021.101808openalex-snapshot
Sparse hop spanners for unit disk graphs
inferred← citeshttps://doi.org/10.1016/j.jda.2008.07.007openalex-snapshot
Light orthogonal networks with constant geometric dilation
inferred← citeshttps://doi.org/10.1109/iccitechnology.2013.6579526openalex-snapshot
Geometric spanners: Recent results and open directions
inferred← citeshttps://doi.org/10.1109/tmc.2011.142openalex-snapshot
Local Construction of Spanners in the 3D Space
inferred← citeshttps://doi.org/10.1137/050635675openalex-snapshot
Improving the Stretch Factor of a Geometric Network by Edge Augmentation
inferred← citeshttps://doi.org/10.1137/080737708openalex-snapshot
On Spanners and Lightweight Spanners of Geometric Graphs
inferred← citeshttps://doi.org/10.1137/s0097539700382947openalex-snapshot
Fast Greedy Algorithms for Constructing Sparse Geometric Spanners
inferred← citeshttps://doi.org/10.1142/s0218195904001366openalex-snapshot
EFFICIENT CONSTRUCTION OF LOW WEIGHTED BOUNDED DEGREE PLANAR SPANNER
inferred← citeshttps://doi.org/10.1142/s1793830916500518openalex-snapshot
Lattice spanners of low degree
inferred← citeshttps://doi.org/10.1145/1064092.1064143openalex-snapshot
Finding the best shortcut in a geometric network
inferred← citeshttps://doi.org/10.1145/1146381.1146413openalex-snapshot
Local approximation schemes for topology control
inferred← citeshttps://doi.org/10.1145/1498698.1564499openalex-snapshot
Experimental study of geometric t -spanners
inferred← citeshttps://doi.org/10.1145/2818375openalex-snapshot
Label Cover Instances with Large Girth and the Hardness of Approximating Basic k -Spanner
inferred← citeshttps://doi.org/10.1145/777792.777794openalex-snapshot
Fault-tolerant geometric spanners
inferred← citeshttps://doi.org/10.1201/9780203497289-9openalex-snapshot
Shortest-Paths Trees
inferred← citeshttps://doi.org/10.1371/journal.pone.0269419openalex-snapshot
The choice of Madrid as the capital of Spain by Philip II in the light of the knowledge of his time: A transport network perspective
inferred← citeshttps://doi.org/10.1631/jzus.2004.0518openalex-snapshot
An efficient parallel algorithm for shortest paths in planar layered digraphs
inferred← citeshttps://doi.org/10.48550/arxiv.1602.04381openalex-snapshot
Lattice spanners of low degree
inferred← citeshttps://doi.org/10.48550/arxiv.cs/0702080openalex-snapshot
Sparse geometric graphs with small dilation
inferred← citeshttps://doi.org/10.48550/arxiv.cs/0703023openalex-snapshot
Computing a Minimum-Dilation Spanning Tree is NP-hard
inferred← citeshttps://doi.org/10.5555/313559.313760openalex-snapshot
Balancing minimum spanning and shortest path trees
inferred← citeshttps://doi.org/10.5860/choice.42-1619aopenalex-snapshot
Spanning trees and optimization problems
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