Randomized parallel communications on an extension of the omega network
Journal of the ACM (JACM)
Designing least-cost nonblocking broadband networks
Journal of Algorithms
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
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
Scaling internet routers using optics
Proceedings of the 2003 conference on Applications, technologies, architectures, and protocols for computer communications
Proceedings of the 2003 conference on Applications, technologies, architectures, and protocols for computer communications
Optimal oblivious routing in polynomial time
Journal of Computer and System Sciences - Special issue: STOC 2003
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
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
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
Load balanced Birkhoff-von Neumann switches, part I: one-stage buffering
Computer Communications
Switched optical backbone for cost-effective scalable core IP networks
IEEE Communications Magazine
Robust solutions of uncertain linear programs
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
Approximability and inapproximability of the minimum certificate dispersal problem
Theoretical Computer Science
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
INFORMS Journal on Computing
The VPN Problem with Concave Costs
SIAM Journal on Discrete Mathematics
Computers and Operations Research
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
Capacitated confluent flows: complexity and algorithms
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Static and dynamic routing under disjoint dominant extreme demands
Operations Research Letters
High-performance routing for hose-based VPNs in multi-domain backbone networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
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We consider the following network design problem. We are given an undirected graph G=(V,E) with edges costs c(e) and a set of terminal nodes W. A hose demand matrix for W is any symmetric matrix [Dij] such that for each i, ∑ 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. and Gupta et al. 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 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 [Hurkens 2005, Grandoni 2007, Fiorini 2007]. Our main theorem establishes that this conjecture is true in general graphs. This also gives the first polynomial time algorithm for the single path VPN problem. We also show that the multipath version of the conjecture is false.