Transitions in geometric minimum spanning trees
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Euclidean spanner graphs with degree four
Discrete Applied Mathematics
Approximating the minimum-degree Steiner tree to within one of optimal
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
A network-flow technique for finding low-weight bounded-degree spanning trees
Journal of Algorithms
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
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
SIAM Journal on Computing
A Matter of Degree: Improved Approximation Algorithms for Degree-Bounded Minimum Spanning Trees
SIAM Journal on Computing
Euclidean Bounded-Degree Spanning Tree Ratios
Discrete & Computational Geometry
Primal-Dual Meets Local Search: Approximating MSTs With Nonuniform Degree Bounds
SIAM Journal on Computing
Minimum Bounded Degree Spanning Trees
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
What would edmonds do? augmenting paths and witnesses for degree-bounded MSTs
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
The Euclidean degree-4 minimum spanning tree problem is NP-hard
Proceedings of the twenty-fifth annual symposium on Computational geometry
Design and optimization of a tiered wireless access network
INFOCOM'10 Proceedings of the 29th conference on Information communications
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
Degree Bounded Network Design with Metric Costs
SIAM Journal on Computing
On the area requirements of Euclidean minimum spanning trees
Computational Geometry: Theory and Applications
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Given n points in the Euclidean plane, the degree-@d minimum spanning tree (MST) problem asks for a spanning tree of minimum weight in which the degree of each vertex is at most @d. The problem is NP-hard for 2@?@d@?3, while the NP-hardness of the problem is open for @d=4. The problem is polynomial-time solvable when @d=5. By presenting an improved approximation analysis for Chan's degree-4 MST algorithm [T. Chan, Euclidean bounded-degree spanning tree ratios, Discrete & Computational Geometry 32 (2004) 177-194], we show that, for any arbitrary collection of points in the Euclidean plane, there always exists a degree-4 spanning tree of weight at most (2+2)/3