From Uncertainty to Nonlinearity: Solving Virtual Private Network via Single-Sink Buy-at-Bulk

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).