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Proceedings 2001 IEEE International Conference on Cluster Computing (2001)
Las Vegas, Nevada
Oct. 14, 2001 to Oct. 17, 2001
ISBN: 0-7695-1390-5
pp: 472
<p>e consider a directed network in which every edge possesses a latency function specifying the time needed to traverse the edge given its congestion. Selfish, noncooperative agents constitute the network traffic and wish to travel from a source s to a sink t as quickly as possible. Since the route chosen by one network user affects the congestion (and hence the latency) experienced by others, we model the problem as a noncooperative game. Assuming each agent controls only a negligible portion of the overall traffic, Nash equilibria in this noncooperative game correspond to s-t flows in which all flow paths have equal latency.</p> <p>A natural measure for the performance of a network used by selfish agents is the common latency experienced by each user in a Nash equilibrium. It is a counterintuitive but well-known fact that removing edges from a network may improve its performance; the most famous example of this phenomenon is the so-called Braess?s Paradox. This fact motivates the following network design problem: given such a network, which edges should be removed to obtain the best possible flow at Nash equilibrium? Equivalently, given a large network of candidate edges to be built, which subnetwork will exhibit the best performance when used selfishly?</p> <p>We give optimal inapproximability results and approximation algorithms for several network design problems of this type. For example, we prove that for networks with n nodes and continuous, nondecreasing latency functions, there is no approximation algorithm for this problem with approximation ratio less than n/2 (unless P = NP). We also prove this hardness result to be best possible by exhibiting an n/2-approximation algorithm. For networks in which the latency of each edge is a linear function of the congestion, we prove that there is no (\frac{4}{3} - \varepsilon)-approximation algorithm for the problem (for any \varepsilon > 0, unless P = NP); the existence of a \frac{4}{3}-approximation algorithm follows easily from existing work, proving this hardness result sharp.</p> <p>Moreover, we prove that an optimal approximation algorithm for these problems is what we call the trivial algorithm: given a network of candidate edges, build the entire network. Roughly, this result implies that the presence of harmful extra edges in a network (a phenomenon that can lead to extremely poor performance in large networks with general latency functions) is impossible to detect efficiently.</p>

T. Roughgarden, "Designing Networks for Selfish Users is Hard," Proceedings 2001 IEEE International Conference on Cluster Computing(FOCS), Las Vegas, Nevada, 2001, pp. 472.
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