Designing least-cost nonblocking broadband networks
Journal of Algorithms
Combinatorial optimization
A constant factor approximation for the single sink edge installation problems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Provisioning a virtual private network: a network design problem for multicommodity flow
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
The Single-Sink Buy-at-Bulk LP Has Constant Integrality Gap
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Approximation Hardness of the Steiner Tree Problem on Graphs
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Simpler and better approximation algorithms for network design
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
An improved approximation algorithm for virtual private network design
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Virtual Private Network Design: A Proof of the Tree Routing Conjecture on Ring Networks
SIAM Journal on Discrete Mathematics
New Approaches for Virtual Private Network Design
SIAM Journal on Computing
Approximating connected facility location problems via random facility sampling and core detouring
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Deterministic Sampling Algorithms for Network Design
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
The VPN Problem with Concave Costs
SIAM Journal on Discrete Mathematics
Improved approximation for single-sink buy-at-bulk
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
A short proof of the VPN Tree Routing Conjecture on ring networks
Operations Research Letters
Design of trees in the hose model: The balanced case
Operations Research Letters
Network design via core detouring for problems without a core
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
From Uncertainty to Nonlinearity: Solving Virtual Private Network via Single-Sink Buy-at-Bulk
Mathematics of Operations Research
Approximation algorithms for single and multi-commodity connected facility location
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Journal of the ACM (JACM)
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We give the first constant factor approximation algorithm for the asymmetric Virtual Private Network $(\textsc{Vpn})$ problem with arbitrary concave costs. We even show the stronger result, that there is always a tree solution of cost at most 2·OPT and that a tree solution of (expected) cost at most 49.84·OPT can be determined in polynomial time. For the case of linear cost we obtain a $(2+\varepsilon\frac{\mathcal R}{\mathcal S})$-approximation algorithm for any fixed *** 0, where $\mathcal{S}$ and $\mathcal{R}$ ($\mathcal{R} \geq \mathcal{S}$) denote the outgoing and ingoing demand, respectively. Furthermore, we answer an outstanding open question about the complexity status of the so called balanced $\textsc{Vpn}$ problem by proving its NP-hardness.