Journal of Algorithms
Introduction to algorithms
Three-dimensional integrated circuit layout
Three-dimensional integrated circuit layout
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Low degree spanning trees of small weight
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
The Delaunay tetrahedralization from Delaunay triangulated surfaces
Proceedings of the eighteenth annual symposium on Computational geometry
Extreme Distances in Multicolored Point Sets
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Steiner hull algorithm for the uniform orientation metrics
Computational Geometry: Theory and Applications
New insights into the OCST problem: integrating node degrees and their location in the graph
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
A PTAS for Node-Weighted Steiner Tree in Unit Disk Graphs
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
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Motivated by practical VLSI routing applications, we study the maximum vertex degree of a minimum spanning tree (MST). We prove that under the Lp norm, the maximum vertex degree over all MSTs is equal to the Hadwiger number of the corresponding unit ball; we show an even tighter bound for MSTs where the maximum degree is minimized. We give the best-known bounds for the maximum MST degree for arbitrary Lp metrics in all dimensions, with a focus on the rectilinear metric in two and three dimensions. We show that for any finite set of points in the Manhattan plane there exists an MST with maximum degree of at most 4, and for three-dimensional Manhattan space the maximum possible degree of a minimum degree MST is either 13 or 14.