Transitions in geometric minimum spanning trees
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Computing Proximity Drawings of Trees in the 3-Dimemsional Space
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Heuristic algorithms for real-time data aggregation in wireless sensor networks
Proceedings of the 2006 international conference on Wireless communications and mobile computing
Polynomial area bounds for MST embeddings of trees
Computational Geometry: Theory and Applications
On the area requirements of Euclidean minimum spanning trees
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Drawing a tree as a minimum spanning tree approximation
Journal of Computer and System Sciences
Succinct greedy drawings do not always exist
GD'09 Proceedings of the 17th international conference on Graph Drawing
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In their seminal paper on geometric minimum spanning trees, Monma and Suri gave a method to embed any tree of maximal degree 5 as a minimum spanning tree in the Euclidean plane. They derived area bounds of O(2k2 × 2k2) for trees of height k and conjectured that an improvement below cn × cn is not possible for some constant c 0. We partially disprove this conjecture by giving polynomial area bounds for arbitrary trees of maximal degree 3 and 4.