Integer and combinatorial optimization
Integer and combinatorial optimization
Approximating the minimum degree spanning tree to within one from the optimal degree
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Primal-dual meets local search: approximating MST's with nonuniform degree bounds
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Journal of Graph Theory
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
Survivable network design with degree or order constraints
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Approximating minimum bounded degree spanning trees to within one of optimal
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Spanning trees with minimum weighted degrees
Information Processing Letters
Additive approximation for bounded degree survivable network design
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Network Design with Weighted Degree Constraints
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
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
On generalizations of network design problems with degree bounds
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Network design with weighted degree constraints
Discrete Optimization
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In this paper, we study the minimum degree minimum spanning tree problem: Given a graph G = (V,E) and a non-negative cost function c on the edges, the objective is to find a minimum cost spanning tree T under the cost function c such that the maximum degree of any node in T is minimized. We obtain an algorithm which returns an MST of maximum degree at most Δ*+k where Δ* is the minimum maximum degree of any MST and k is the distinct number of costs in any MST of G. We use a lower bound given by a linear programming relaxation to the problem and strengthen known graph-theoretic results on minimum degree subgraphs [3,5] to prove our result. Previous results for the problem [1,4] used a combinatorial lower bound which is weaker than the LP bound we use.