Designing least-cost nonblocking broadband networks
Journal of Algorithms
Combinatorial optimization
Robust Solutions to Least-Squares Problems with Uncertain Data
SIAM Journal on Matrix Analysis and Applications
Mathematics of Operations Research
A flexible model for resource management in virtual private networks
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
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
Algorithms for provisioning virtual private networks in the hose model
IEEE/ACM Transactions on Networking (TON)
Robust Solutions to Uncertain Semidefinite Programs
SIAM Journal on Optimization
Minimizing Congestion in General Networks
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Networks new economical virtual private
Communications of the ACM - E-services: a cornucopia of digital offerings ushers in the next Net-based evolution
Simpler and better approximation algorithms for network design
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Routing, merging and sorting on parallel models of computation
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Universal schemes for parallel communication
STOC '81 Proceedings of the thirteenth 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
Provisioning virtual private networks under traffic uncertainty
Networks - Special Issue on Multicommodity Flows and Network Design
Hardness of robust network design
Networks
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
Optimal hierarchical decompositions for congestion minimization in networks
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
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
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
The VPN Problem with Concave Costs
SIAM Journal on Discrete Mathematics
Provisioning a virtual private network under the presence of non-communicating groups
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
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
Robust solutions of uncertain linear programs
Operations Research Letters
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We consider the following network design problem. We are given an undirected graph G = (V,E) with edge costs c(e) and a set of terminal nodes W ⊆ V. A hose demand matrix is any symmetric matrix D, indexed by the terminals, such that for each i ∈ W, ∑j≠i Dij ≤ 1. We must compute the minimum-cost edge capacities that are able to support the oblivious routing of every hose matrix in the network. An oblivious routing template, in this context, is a simple path Pij for each pair i,j ∈ W. Given such a template, if we are to route a demand matrix D, then for each i,j, we send Dij units of flow along each Pij. Fingerhut et al. [1997] and Gupta et al. [2001] obtained a 2-approximation for this problem, using a solution template in the form of a tree. It has been widely asked and subsequently conjectured [Italiano et al. 2006] that this solution actually results in the optimal capacity for the single-path VPN design problem; this has become known as the VPN Conjecture. The conjecture has previously been proven for some restricted classes of graphs [Fingerhut et al. 1997; Fiorini et al. 2007; Grandoni et al. 2008; Hurkens et al. 2007]. Our main theorem establishes that this conjecture is true in general graphs. This also has the implication that the single-path VPN problem is solvable in polynomial time. A natural fractional version of the conjecture had also been proposed [Hurkens et al. 2007]. In this version, the routing may split flow between many paths, in specified proportions. We demonstrate that this multipath version of the conjecture is in fact false. The multipath and single path versions of the VPN problem are essentially direct analogues of the randomized and nonrandomized versions of oblivious routing schemes for minimizing congestion for permutation routing [Borodin and Hopcroft 1982; Valiant 1982].