Transitions in geometric minimum spanning trees
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
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Journal of the ACM (JACM)
Triangulations without minimum-weight drawing
Information Processing Letters
A lower bound for &bgr;-skeleton belonging to minimum weight triangulations
Computational Geometry: Theory and Applications
The drawability problem for minimum weight triangulations
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computing Proximity Drawings of Trees in the 3-Dimemsional Space
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Proximity Drawings of Outerplanar Graphs
GD '96 Proceedings of the Symposium on Graph Drawing
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
Heuristic algorithms for real-time data aggregation in wireless sensor networks
Proceedings of the 2006 international conference on Wireless communications and mobile computing
Handbook of Graph Drawing and Visualization (Discrete Mathematics and Its Applications)
Handbook of Graph Drawing and Visualization (Discrete Mathematics and Its Applications)
Area-efficient planar straight-line drawings of outerplanar graphs
Discrete Applied Mathematics
Degree-bounded minimum spanning trees
Discrete Applied Mathematics
Small Area Drawings of Outerplanar Graphs
Algorithmica
The Euclidean degree-4 minimum spanning tree problem is NP-hard
Proceedings of the twenty-fifth annual symposium on Computational geometry
On Open Rectangle-of-Influence Drawings of Planar Graphs
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Polynomial area bounds for MST embeddings of trees
GD'07 Proceedings of the 15th international conference on Graph drawing
Computing β-drawings of 2-outerplane graphs in linear time
WALCOM'08 Proceedings of the 2nd international conference on Algorithms and computation
The approximate rectangle of influence drawability problem
GD'12 Proceedings of the 20th international conference on Graph Drawing
On the area requirements of Euclidean minimum spanning trees
Computational Geometry: Theory and Applications
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In their seminal paper on geometric minimum spanning trees, Monma and Suri (1992) [31] showed how to embed any tree of maximum degree 5 as a minimum spanning tree in the Euclidean plane. The embeddings provided by their algorithm require area O(2^n^^^2)xO(2^n^^^2) and the authors conjectured that an improvement below c^nxc^n is not possible, for some constant c0. In this paper, we show how to construct MST embeddings of arbitrary trees of maximum degree 3 and 4 within polynomial area.