Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
A matter of degree: improved approximation algorithms for degree-bounded minimum spanning trees
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Comparison of Algorithms for the Degree Constrained Minimum Spanning Tree
Journal of Heuristics
Proceedings of the EvoWorkshops on Applications of Evolutionary Computing
Spanning Trees with Bounded Number of Branch Vertices
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Euclidean bounded-degree spanning tree ratios
Proceedings of the nineteenth annual symposium on Computational geometry
Using Lagrangian dual information to generate degree constrained spanning trees
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Degree-bounded minimum spanning trees
Discrete Applied Mathematics
VNS and second order heuristics for the min-degree constrained minimum spanning tree problem
Computers and Operations Research
The Euclidean degree-4 minimum spanning tree problem is NP-hard
Proceedings of the twenty-fifth annual symposium on Computational geometry
Using Lagrangian dual information to generate degree constrained spanning trees
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
There are spanning spiders in dense graphs (and we know how to find them)
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Theoretical Computer Science
Degree Bounded Network Design with Metric Costs
SIAM Journal on Computing
Degree-bounded minimum spanning tree for unit disk graph
Theoretical 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
A push-relabel algorithm for approximating degree bounded MSTs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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Given $n$ points in the plane, the degree-$K$ spanning-tree problem asks for a spanning tree of minimum weight in which the degree of each vertex is at most $K$. This paper addresses the problem of computing low-weight degree-$K$ spanning trees for $K2$. It is shown that for an arbitrary collection of $n$ points in the plane, there exists a spanning tree of degree 3 whose weight is at most 1.5 times the weight of a minimum spanning tree. It is shown that there exists a spanning tree of degree 4 whose weight is at most 1.25 times the weight of a minimum spanning tree. These results solve open problems posed by Papadimitriou and Vazirani. Moreover, if a minimum spanning tree is given as part of the input, the trees can be computed in $O(n)$ time. The results are generalized to points in higher dimensions. It is shown that for any $d \ge 3$, an arbitrary collection of points in $\Re^d$ contains a spanning tree of degree 3 whose weight is at most 5/3 times the weight of a minimum spanning tree. This is the first paper that achieves factors better than 2 for these problems.