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
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
Approximability of robust network design
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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
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
Steiner Tree Approximation via Iterative Randomized Rounding
Journal of the ACM (JACM)
Journal of the ACM (JACM)
A new approximation algorithm for the Selective Single-Sink Buy-at-Bulk problem in network design
Journal of Combinatorial Optimization
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Virtual private network design is the following NP-hard problem. We are given a communication network represented as a weighted graph with thresholds on the nodes which represent the amount of flow that a node can send to and receive from the network. The task is to reserve capacities at minimum cost and to specify paths between every ordered pair of nodes such that all valid traffic-matrices can be routed along the corresponding paths. Recently, this network design problem has received considerable attention in the literature. It is motivated by the fact that the exact amount of flow which is exchanged between terminals is not known in advance and prediction is often elusive. The main contributions of this paper are as follows: (1) Using Hu's 2-commodity flow theorem, we provide a new and considerably stronger lower bound on the cost of an optimum solution. With this lower bound we reanalyze a simple routing scheme which has been described in the literature many times, and provide an improved upper bound on its approximation ratio. (2) We present a new randomized approximation algorithm. In contrast to earlier approaches from the literature, the resulting solution does not have tree structure. A combination of our new algorithm with the simple routing scheme yields an expected performance ratio of $3.79$ for virtual private network design. This is a considerable improvement of the previously best known $5.55$-approximation result [A. Gupta, A. Kumar, and T. Roughgarden, Simpler and better approximation algorithms for network design, in Proceedings of the ACM Symposium on Theory of Computing, ACM, New York, 2003, pp. 365-372]. (3) Our VPND algorithm uses a Steiner tree approximation algorithm as a subroutine. It is known that an optimum Steiner tree can be computed in polynomial time if the number of terminals is logarithmic. Replacing the approximate Steiner tree computation with an exact one whenever the number of terminals is sufficiently small, we finally reduce the approximation ratio to $3.55$. To the best of our knowledge, this is the first time that a nontrivial result from exact (exponential) algorithms leads to an improved polynomial-time approximation algorithm.