The VPN Problem with Concave Costs

We consider the following network design problem. We are given an undirected network with costs on the edges, a set of terminals, and an upper bound for each terminal limiting the cumulative amount of traffic it can send or receive. The task is to select a path for each unordered pair of terminals and reserve minimum cost capacities so that all the sets of traffic demands that satisfy the bounds can be routed along the selected paths. When the contribution of an edge to the total cost is proportional to the capacity reservation for that edge, this problem is referred to as the symmetric Virtual Private Network Design (sVPN) problem. Goyal, Olver and Shepherd (Proc. STOC, 2008) showed that there always exists an optimal solution to sVPN that is a tree solution, i.e., such that the support of the capacity reservation is a tree. Combining this with previous results by Fingerhut, Suri and Turner (J. Alg., 1997) and Gupta, Kleinberg, Kumar, Rastogi and Yener (Proc. STOC, 2001), sVPN can be ...

• Type: Journal
• Year: 2010
• Where: SIAMDM
• Authors: Samuel Fiorini, Gianpaolo Oriolo, Laura Sanità, Dirk Oliver Theis
• Keywords: Capacity Reservation, Network Design, SIAMDM 2010, Virtual Private Network