The symmetric Virtual Private Network Design (VPND) problem is concerned with buying capacity on links (edges) in a communication network such that certain traffic demands can be met. We investigate a natural generalization of VPND where the cost per unit of capacity may decrease if a larger amount of capacity is reserved (economies of scale principle). The growth of the cost of capacity is modelled by a non-decreasing concave function f. We call the problem the concave symmetric Virtual Private Network Design (cVPND) problem. After showing that a generalization of the so-called Pyramidal Routing problem and hence also the cVPND have the so-called tree routing property, we study approximation algorithms for cVPND. For general f, using known results on the so-called Single Source Buy at Bulk problem by Grandoni and Italiano, we give a randomized 24.92-approximation algorithm.
Cite
@article{arxiv.0812.2355,
title = {The Virtual Private Network Design Problem with Concave Costs (Oberwolfach abstract)},
author = {Samuel Fiorini and Gianpaolo Oriolo and Laura Sanità and Dirk Oliver Theis},
journal= {arXiv preprint arXiv:0812.2355},
year = {2008}
}