When trees collide: an approximation algorithm for the generalized Steiner problem on networks
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
A general approximation technique for constrained forest problems
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
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 General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
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
A Matter of Degree: Improved Approximation Algorithms for Degree-Bounded Minimum Spanning Trees
SIAM Journal on Computing
Approximation Through Local Optimality: Designing Networks with Small Degree
Proceedings of the 12th Conference on Foundations of Software Technology and Theoretical Computer Science
End system multicast protocol for collaborative virtual environments
Presence: Teleoperators and Virtual Environments - Special issue: Advances in collaborative virtual environments
End System Multicast routing for multi-party videoconferencing applications
Computer Communications
A minimum spanning tree algorithm for efficient P2P video streaming system
ICACT'10 Proceedings of the 12th international conference on Advanced communication technology
Matroidal degree-bounded minimum spanning trees
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
On degree constrained shortest paths
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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
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
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
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Chain-Constrained spanning trees
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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We present a new bicriteria approximation algorithm for the degree-bounded minimum-cost spanning tree problem: Given an undirected graph with nonnegative edge weights and degree bounds Bv 1 for all vertices v, find a spanning tree T of minimum total edge-cost such that the maximum degree of each node v in T is at most Bv. Our algorithm finds a tree in which the degree of each node v is O(Bv + log n) and the total edge-cost is at most a constant times the cost of any tree that obeys all degree constraints.Our previous algorithm[9] with similar guarantees worked only in the case of uniform degree bounds (i.e. Bv=B for all vertices v). While the new algorithm is based on ideas from Lagrangean relaxation as is our previous work, it does not rely on computing a solution to a linear program. Instead it uses a repeated application of Kruskal's MST algorithm interleaved with a combinatorial update of approximate Lagrangean node-multipliers maintained by the algorithm. These updates cause subsequent repetitions of the spanning tree algorithm to run for longer and longer times, leading to overall progress and a proof of the performance guarantee.