Minimum concave-cost network flow problems: applications, complexity, and algorithms
Annals of Operations Research
Designing least-cost nonblocking broadband networks
Journal of Algorithms
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
Building Steiner trees with incomplete global knowledge
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Approximation via cost sharing: Simpler and better approximation algorithms for network design
Journal of the ACM (JACM)
Virtual Private Network Design: A Proof of the Tree Routing Conjecture on Ring Networks
SIAM Journal on Discrete Mathematics
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
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
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
From Uncertainty to Nonlinearity: Solving Virtual Private Network via Single-Sink Buy-at-Bulk
Mathematics of Operations Research
An exact algorithm for robust network design
INOC'11 Proceedings of the 5th international conference on Network optimization
Models and algorithms for robust network design with several traffic scenarios
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Journal of the ACM (JACM)
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Only recently Goyal, Olver, and Shepherd [Proc. STOC, ACM, New York, 2008] proved that the symmetric virtual private network design (sVPN) problem has the tree routing property, namely, that there always exists an optimal solution to the problem whose support is a tree. Combining this with previous results by Fingerhut, Suri, and Turner [J. Algorithms, 24 (1997), pp. 287-309] and Gupta et al. [Proc. STOC, ACM, New York, 2001], sVPN can be solved in polynomial time. In this paper we investigate an APX-hard generalization of sVPN, where the contribution of each edge to the total cost is proportional to some non-negative, concave, and nondecreasing function of the capacity reservation. We show that the tree routing property extends to the new problem and give a constant-factor approximation algorithm for it. We also show that the undirected uncapacitated single-source minimum concave-cost flow problem has the tree routing property when the cost function has some property of symmetry.