Designing least-cost nonblocking broadband networks
Journal of Algorithms
Combinatorial optimization
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A flexible model for resource management in virtual private networks
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
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
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
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
Primal-Dual Algorithms for Connected Facility Location Problems
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Simpler and better approximation algorithms for network design
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Cost-distance: two metric network design
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Building Steiner trees with incomplete global knowledge
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
An improved approximation algorithm for virtual private network design
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Simple cost sharing schemes for multicommodity rent-or-buy and stochastic Steiner tree
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Approximation via cost sharing: Simpler and better approximation algorithms for network design
Journal of the ACM (JACM)
Sharing the cost more efficiently: Improved approximation for multicommodity rent-or-buy
ACM Transactions on Algorithms (TALG)
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
Stochastic analyses for online combinatorial optimization problems
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
On the Complexity of the Asymmetric VPN Problem
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
A Constant Factor Approximation for the Single Sink Edge Installation Problem
SIAM Journal on Computing
A constant approximation algorithm for the a priori traveling salesman problem
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
An improved LP-based approximation for steiner tree
Proceedings of the forty-second ACM symposium on Theory of computing
Connected facility location via random facility sampling and core detouring
Journal of Computer and System Sciences
Network design via core detouring for problems without a core
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
The VPN Problem with Concave Costs
SIAM Journal on Discrete Mathematics
Stochastic steiner trees without a root
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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
Steiner Tree Approximation via Iterative Randomized Rounding
Journal of the ACM (JACM)
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The virtual private network problem (VPN) models scenarios in which traffic is uncertain or rapidly changing. The goal is supporting at minimum cost a given family of traffic matrices, which are implicitly given by upper bounds on the ingoing and outgoing traffic at each node. Costs are classically defined by a linear function (linear VPN), but we consider here also the more general case of concave increasing costs (concave VPN). In this paper we give the first constant factor approximation for concave VPN, and we improve the best-known approximation factor for linear VPN. Our approximation results build on a novel reduction, based on König's theorem, which allows us to turn uncertainty of traffic into nonlinearity of the objective function. This way, we are able to reduce linear VPN and concave VPN to the single-sink rent-or-buy problem (SROB) and the single-sink buy-at-bulk problem (SSBB), respectively. Using the machinery developed for the latter two problems plus additional ideas, we are able to improve the approximation ratio for VPN. Along the way we also obtain, among other results, an improved approximation algorithm for SSBB and a tighter bound on the gap between the costs of arbitrary solutions and tree solutions for VPN. Furthermore, solving an open problem, we show that VPN remains NP-hard even in the balanced case, where the sum of ingoing and outgoing traffic bounds is equal.