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
On the area requirements of Euclidean minimum spanning trees
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Narrow-Shallow-Low-Light Trees with and without Steiner Points
SIAM Journal on Discrete Mathematics
Degree Bounded Network Design with Metric Costs
SIAM Journal on Computing
Degree-bounded minimum spanning tree for unit disk graph
Theoretical Computer Science
On the area requirements of Euclidean minimum spanning trees
Computational Geometry: Theory and Applications
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Let τK be the worst-case (supremum) ratio of the weight of the minimum degree-K spanning tree to the weight of the minimum spanning tree, over all finite point sets in the Euclidean plane. It is known that τ2 = 2 and τ5 = 1. In STOC ‘94, Khuller, Raghavachari, and Young established the following inequalities: 1.103 3 \le 1.5 and 1.035 4 \le 1.25. We present the first improved upper bounds: τ3 4 K(d) be the analogous ratio in d-dimensional space. Khuller et al. showed thatτ3(d) 3(d)