Transitions in geometric minimum spanning trees
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Area Requirement of Gabriel Drawings
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
Euclidean Bounded-Degree Spanning Tree Ratios
Discrete & Computational Geometry
Degree-bounded minimum spanning trees
Discrete Applied Mathematics
The Euclidean degree-4 minimum spanning tree problem is NP-hard
Proceedings of the twenty-fifth annual symposium on Computational geometry
Polynomial area bounds for MST embeddings of trees
GD'07 Proceedings of the 15th international conference on Graph drawing
Approximate proximity drawings
GD'11 Proceedings of the 19th international conference on Graph Drawing
The approximate rectangle of influence drawability problem
GD'12 Proceedings of the 20th international conference on Graph Drawing
Approximate proximity drawings
Computational Geometry: Theory and Applications
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In their seminal paper on Euclidean minimum spanning trees [Discrete & Computational Geometry, 1992], Monma and Suri proved that any tree of maximum degree 5 admits a planar embedding as a Euclidean minimum spanning tree. Their algorithm constructs embeddings with exponential area; however, the authors conjectured that cn × cn area is sometimes required to embed an n-vertex tree of maximum degree 5 as a Euclidean minimum spanning tree, for some constant c 1. In this paper, we prove the first exponential lower bound on the area requirements for embedding trees as Euclidean minimum spanning trees.