Approximating the minimum-degree Steiner tree to within one of optimal
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
Bicriteria network design problems
Journal of Algorithms
Generalized submodular cover problems and applications
Theoretical Computer Science
A polylogarithmic approximation algorithm for the group Steiner tree problem
Journal of Algorithms
Approximation Through Local Optimality: Designing Networks with Small Degree
Proceedings of the 12th Conference on Foundations of Software Technology and Theoretical Computer Science
Minimum Bounded Degree Spanning Trees
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Approximating minimum bounded degree spanning trees to within one of optimal
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Additive approximation for bounded degree survivable network design
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Survivable Network Design with Degree or Order Constraints
SIAM Journal on Computing
Additive Guarantees for Degree-Bounded Directed Network Design
SIAM Journal on Computing
Approximating directed weighted-degree constrained networks
Theoretical Computer Science
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
Degree-Constrained node-connectivity
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
On some network design problems with degree constraints
Journal of Computer and System Sciences
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We study several network design problems with degree constraints. For the degree-constrained 2-connected subgraph problem we obtain a factor 6 violation for the degrees with 4 approximation for the cost. This improves upon the logarithmic degree violation and no cost guarantee obtained by Feder, Motwani, and Zhu (2006). Then we consider the problem of finding an arborescence with at least k terminals and with minimum maximum outdegree. We show that the natural LP-relaxation has a gap of Ω(√k) or Ω(n1/4) with respect to the multiplicative degree bound violation. We overcome this hurdle by a combinatorial O(√(k log k)/Δ*)-approximation algorithm, where Δ* denotes the maximum degree in the optimum solution. We also give an Ω(log n) lower bound on approximating this problem. Then we consider the undirected version of this problem, however, with an extra diameter constraint, and give an Ω(log n) lower bound on the approximability of this version. Finally, we consider a closely related prize-collecting degree-constrained Steiner Network problem. We obtain several results in this direction by reducing the prize-collecting variant to the regular one.