 
Summary: The Hardness of Network Design for
Unsplittable Flow with Selfish Users
Yossi Azar 1 and Amir Epstein 2
1 School of Computer Science, TelAviv University, TelAviv, 69978, Israel.
azar@tau.ac.il #
2 School of Computer Science, TelAviv University, TelAviv, 69978, Israel.
amirep@tau.ac.il ##
Abstract. In this paper we consider the network design for selfish users
problem, where we assume the more realistic unsplittable model in which
the users can have general demands and each user must choose a single
path between its source and its destination. This model is also called
atomic (weighted) network congestion game. The problem can be pre
sented as follows : given a network, which edges should be removed to
minimize the cost of the worst Nash equilibrium?
We consider both computational issues and existential issues (i.e. the
power of network design). We give inapproximability results and ap
proximation algorithms for this network design problem. For networks
with linear edge latency functions we prove that there is no approx
imation algorithm for this problem with approximation ratio less then
(3+ # 5)/2 # 2.618 unless P = NP . We also show that for networks with
