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
Computational Geometry: Theory and Applications
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In their seminal paper on Euclidean minimum spanning trees, Monma and Suri (1992) 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 there exist n-vertex trees of maximum degree 5 that require c^nxc^n area to be embedded as Euclidean minimum spanning trees, for some constant c1. In this paper, we prove the first exponential lower bound on the area requirements for embedding trees as Euclidean minimum spanning trees.