Many birds with one stone: multi-objective approximation algorithms
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
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 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
Low-Degree Spanning Trees of Small Weight
SIAM Journal on Computing
The Directed Minimum-Degree Spanning Tree Problem
FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
Euclidean bounded-degree spanning tree ratios
Proceedings of the nineteenth annual symposium on Computational geometry
Primal-dual meets local search: approximating MST's with nonuniform degree bounds
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
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
A distributed approximation algorithm for the minimum degree minimum weight spanning trees
Journal of Parallel and Distributed Computing
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
Degree-bounded minimum spanning trees
Discrete Applied Mathematics
Delegate and conquer: an LP-based approximation algorithm for minimum degree 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
Operations Research Letters
Hi-index | 0.01 |
Given a graph and degree upper bounds on vertices, the BDMST problem requires us to find the minimum cost spanning tree respecting the given degree bounds.Könemann and Ravi [10,11] give bicriteria approximation algorithms for the problem using local search techniques of Fischer [5]. For a graph with a cost C, degree B spanning tree, and parameters b, w 1, their algorithm produces a tree whose cost is at most wC and whose degree is at most $\frac{w}{w-1}bB + \log_b n.$ We give a polynomial-time algorithm that finds a tree of optimal cost and with maximum degree at most bB + 2(b+1)logbn. We also give a quasi-polynomial algorithm which produces a tree of optimal cost C and maximum degree bounded by B + O(log n/loglog n). Our algorithms work when there are upper as well as lower bounds on the degrees of the vertices.