Approximating the minimum-degree Steiner tree to within one of optimal
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Bicriteria network design problems
Journal of Algorithms
Approximation algorithms for directed Steiner 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
On the terminal Steiner tree problem
Information Processing Letters
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Splitters and near-optimal derandomization
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of 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
On the full and bottleneck full Steiner tree problems
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Additive Guarantees for Degree-Bounded Directed Network Design
SIAM Journal on Computing
Iterative Methods in Combinatorial Optimization
Iterative Methods in Combinatorial Optimization
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
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
Prize-Collecting steiner network problems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Hi-index | 0.00 |
We study several network design problems with degree constraints. For the minimum-cost Degree-Constrained 2-Node-Connected Subgraph problem, we obtain the first non-trivial bicriteria approximation algorithm, with 5b(v)+3 violation for the degrees and a 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 @W(k) or @W(n^1^/^4) with respect to the multiplicative degree bound violation. We overcome this hurdle by a combinatorial O((klogk)/@D^@?)-approximation algorithm, where @D^@? denotes the maximum degree in the optimum solution. We also give an @W(logn) lower bound on approximating this problem. Then we consider the undirected version of this problem, however, with an extra diameter constraint, and give an @W(logn) lower bound on the approximability of this version. We also consider a closely related Prize-Collecting Degree-Constrained Edge-Connectivity Survivable Network problem, and obtain several results in this direction by reducing the prize-collecting variant to the regular one. Finally, we consider the Terminal Steiner Tree problem, which is a simple variant of the Degree-Constrained Steiner Tree problem, when some terminals are required to be leaves. We show that this seemingly simple problem is equivalent to the Group Steiner Tree problem.