Fast algorithms for convex quadratic programming and multicommodity flows
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Convex separable optimization is not much harder than linear optimization
Journal of the ACM (JACM)
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
P-Complete Approximation Problems
Journal of the ACM (JACM)
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximation algorithms
Designing Networks for Selfish Users is Hard
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Convex Optimization
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Selfish Routing and the Price of Anarchy
Selfish Routing and the Price of Anarchy
Braess's paradox in large random graphs
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
On the severity of Braess's paradox: designing networks for selfish users is hard
Journal of Computer and System Sciences - Special issue on FOCS 2001
Convergence to approximate Nash equilibria in congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient Methods for Selfish Network Design
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Efficient methods for selfish network design
Theoretical Computer Science
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A picturesque way to see a large network of links shared by many infinitesimally small selfish users is as a large pipeline infrastructure with users as liquid molecules flowing into it. When the owner of such a selfishly congested network tries to improve its flow speed, the common sense suggests to focus and fix links that seem older and slower. Contrary to this belief, Braess's paradox illustrates that destroying a part of a network, even of the most expensive infrastructure, can improve its performance. So a wise owner should take steps cautiously and benefit by exploiting the nature of this paradox. There are a few natural approaches for improving network performance. A simple approach, not requiring any network modifications, is Stackelberg routing. The network owner dictatorially controls a small fraction of flow, aiming to improve the induced routing performance of the remaining selfish flow. Unfortunately, there are examples of unboundedly bad performance under any possible control attempt made by the owner. Another side-effect is that the dictatorially controlled flow is usually sacrificed through slower paths, compared to the latency faced by the remaining free flow. An alternative approach is to introduce economic incentives, usually modeled as flow-dependent per-unit-of-flow tolls, that influence the users' selfish choices toward improving performance. However, the idea of tolls is not appealing to the users, since large tolls increase the users' disutility: routing time plus tolls paid. A simple and easy to implement way out from the above side effects is to exploit the essence of Braess's paradox toward improving network performance. In this work we survey some recent results about this paradox, eluding some recent hardness results under the most wide and natural assumptions about the link latencies of input network.