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
Approximating the minimum-degree Steiner tree to within one of optimal
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
Algorithms for finding low degree structures
Approximation algorithms for NP-hard problems
Approximation algorithms
A Matter of Degree: Improved Approximation Algorithms for Degree-Bounded Minimum Spanning Trees
SIAM Journal on Computing
Degree-constrained multicasting in point-to-point networks
INFOCOM '95 Proceedings of the Fourteenth Annual Joint Conference of the IEEE Computer and Communication Societies (Vol. 1)-Volume - Volume 1
Primal-Dual Meets Local Search: Approximating MSTs With Nonuniform Degree Bounds
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A survey of combinatorial optimization problems in multicast routing
Computers and Operations Research
Minimum Bounded Degree Spanning Trees
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
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
Additive guarantees for degree bounded directed network design
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Degree bounded matroids and submodular flows
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
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
Additive guarantees for degree bounded directed network design
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Proceedings of the fifth international workshop on Foundations of mobile computing
Network Design with Weighted Degree Constraints
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Online and stochastic survivable network design
Proceedings of the forty-first annual ACM symposium on Theory of computing
Deploying mesh nodes under non-uniform propagation
INFOCOM'10 Proceedings of the 29th conference on Information communications
Tree embeddings for two-edge-connected network design
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximating minimum cost source location problems with local vertex-connectivity demands
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Network-design with degree constraints
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Degree Bounded Network Design with Metric Costs
SIAM Journal on Computing
Matroidal degree-bounded minimum spanning trees
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Prize-collecting steiner networks via iterative rounding
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Improved algorithm for degree bounded survivable network design problem
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
On generalizations of network design problems with degree bounds
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Degree-Constrained node-connectivity
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Network design with weighted degree constraints
Discrete Optimization
On some network design problems with degree constraints
Journal of Computer and System Sciences
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We study a general network design problem with additional degree constraints. Given connectivity requirements ruv for all pairs of vertices, a Steiner network is a graph in which there are at least ruv edge-disjoint paths between u and v for all pairs of vertices u,v. In the MINIMUM BOUNDED-DEGREE STEINER NETWORK problem, we are given an undirected graph G with an edge cost for each edge, a connectivity requirement ruv for each pair of vertices u and v, and a degree upper bound for each vertex v. The task is to find a minimum cost Steiner network which satisfies all the degree upper bounds. The aim of this paper is to design approximation algorithms that minimize the total cost and the degree violation simultaneously. Our main results are the following: There is a polynomial time algorithm which returns a Steiner forest of cost at most 2 OPT and the degree violation at each vertex is at most 3 ,where OPT is the cost of an optimal solution which satisfies all the degree bounds. There is a polynomial time algorithm which returns a Steiner network of cost at most 2 OPT and the degree violation at each vertex is at most 6r max +3 ,where OPT is the cost of an optimal solution which satisfies all the degree bounds, and r max := max u,v {r uv}. These results achieve the best known guarantees for both the total cost and the degree violation simultaneously. As corollaries, these results provide the first additive approximation algorithms for finding low degree subgraphs including Steiner forests, k -edge-connected subgraphs, and Steiner networks. The algorithms develop on the iterative relaxation method applied to a natural linear programming relaxation as in [10, 16, 22]. The new algorithms avoid paying a multiplicative factor of two on the degree bounds even though the algorithm can only pick edges with fractional value 1/2 . This is based on a stronger characterization of the basic so-algorithm is nearly tight.