Transitions in geometric minimum spanning trees
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Computing Proximity Drawings of Trees in the 3-Dimemsional Space
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Proximity Constraints and Representable Trees
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Polynomial area bounds for MST embeddings of trees
GD'07 Proceedings of the 15th international conference on Graph drawing
Universality considerations in VLSI circuits
IEEE Transactions on Computers
Drawing trees with perfect angular resolution and polynomial area
GD'10 Proceedings of the 18th 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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We introduce and study (1+@e)-EMST drawings, i.e., planar straight-line drawings of trees such that, for any fixed @e0, the distance between any two vertices is at least 11+@e the length of the longest edge in the path connecting them. (1+@e)-EMST drawings are good approximations of Euclidean minimum spanning trees. While it is known that only trees with bounded degree have a Euclidean minimum spanning tree realization, we show that every tree T has a (1+@e)-EMST drawing for any given @e0. We also present drawing algorithms that compute (1+@e)-EMST drawings of trees with bounded degree in polynomial area. As a byproduct of one of our techniques, we improve the best known area upper bound for Euclidean minimum spanning tree realizations of complete binary trees.