 
Summary: Hardness of BuyatBulk Network Design
Matthew Andrews
Bell Laboratories
Murray Hill, NJ 07974
andrews@research.belllabs.com
Abstract
We consider the BuyatBulk network design problem in
which we wish to design a network for carrying multicom
modity demands from a set of source nodes to a set of des
tination nodes. The key feature of the problem is that the
cost of capacity on each edge is concave and hence exhibits
economies of scale. If the cost of capacity per unit length
can be different on different edges then we say that the prob
lem is nonuniform. The problem is uniform otherwise.
We show that for any constant
, if NP 6
ZPT IME(n polylog n ) then there is no O(log 1
2
N)
approximation algorithm for nonuniform BuyatBulk net
work design and there is no O(log 1
4
N)approximation
