Convex separable optimization is not much harder than linear optimization
Journal of the ACM (JACM)
Simple strategies for large zero-sum games with applications to complexity theory
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Achieving network optima using Stackelberg routing strategies
IEEE/ACM Transactions on Networking (TON)
Journal of the ACM (JACM)
The price of anarchy is independent of the network topology
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Playing large games using simple strategies
Proceedings of the 4th ACM conference on Electronic commerce
Stackelberg Scheduling Strategies
SIAM Journal on Computing
A stronger bound on Braess's Paradox
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Edge Pricing of Multicommodity Networks for Heterogeneous Selfish Users
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Tolls for Heterogeneous Selfish Users in Multicommodity Networks and Generalized Congestion Games
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
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
How much can taxes help selfish routing?
Journal of Computer and System Sciences - Special issue on network algorithms 2005
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
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
Taxes for linear atomic congestion games
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Stackelberg strategies for atomic congestion games
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Cost-balancing tolls for atomic network congestion games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Braess's paradox, fibonacci numbers, and exponential inapproximability
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
The hardness of network design for unsplittable flow with selfish users
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Selfish splittable flows and NP-completeness
Computer Science Review
Random Structures & Algorithms
On the hardness of network design for bottleneck routing games
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
On the hardness of network design for bottleneck routing games
Theoretical Computer Science
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Intuitively, Braess's paradox states that destroying a part of a network may improve the common latency of selfish flows at Nash equilibrium. Such a paradox is a pervasive phenomenon in real-world networks. Any administrator, who wants to improve equilibrium delays in selfish networks, is facing some basic questions: (i) Is the network paradox-ridden ? (ii) How can we delete some edges to optimize equilibrium flow delays? (iii) How can we modify edge latencies to optimize equilibrium flow delays? Unfortunately, such questions lead to NP-hard problems in general. In this work, we impose some natural restrictions on our networks, e.g. we assume strictly increasing linear latencies. Our target is to formulate efficient algorithms for the three questions above. We manage to provide: A polynomial-time algorithm that decides if a network is paradox-ridden, when latencies are linear and strictly increasing. A reduction of the problem of deciding if a network with arbitrary linear latencies is paradox-ridden to the problem of generating all optimal basic feasible solutions of a Linear Program that describes the optimal traffic allocations to the edges with constant latency. An algorithm for finding a subnetwork that is almost optimal wrt equilibrium latency. Our algorithm is subexponential when the number of paths is polynomial and each path is of polylogarithmic length. A polynomial-time algorithm for the problem of finding the best subnetwork, which outperforms any known approximation algorithm for the case of strictly increasing linear latencies. A polynomial-time method that turns the optimal flow into a Nash flow by deleting the edges not used by the optimal flow, and performing minimal modifications to the latencies of the remaining ones. Our results provide a deeper understanding of the computational complexity of recognizing the Braess's paradox most severe manifestations, and our techniques show novel ways of using the probabilistic method and of exploiting convex separable quadratic programs.