The Virtual Private Network Design Problem with Concave Costs (Oberwolfach abstract)

TL;DR

This paper studies a generalized VPN design problem where capacity costs decrease with larger reservations, modeling economies of scale, and provides approximation algorithms for solving it.

Contribution

It introduces the concave VPND problem, proves it has the tree routing property, and offers a randomized approximation algorithm.

Findings

The cVPND problem has the tree routing property.

A 24.92-approximation algorithm is developed for general concave cost functions.

The approach extends known results from the Single Source Buy at Bulk problem.

Abstract

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.