Data structures and network algorithms
Data structures and network algorithms
Inefficiency of Nash equilibria
Mathematics of Operations Research
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Counterexamples for comparisons of queues with finite waiting rooms
Queueing Systems: Theory and Applications
Pricing in computer networks: motivation, formulation, and example
IEEE/ACM Transactions on Networking (TON)
Making greed work in networks: a game-theoretic analysis of switch service disciplines
IEEE/ACM Transactions on Networking (TON)
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
Approximation algorithms for finding highly connected subgraphs
Approximation algorithms for NP-hard problems
Algorithms for finding low degree structures
Approximation algorithms for NP-hard problems
Achieving network optima using Stackelberg routing strategies
IEEE/ACM Transactions on Networking (TON)
Congestion resulting from increased capacity in single-server queueing networks
IEEE/ACM Transactions on Networking (TON)
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
The designer's perspective to atomic noncooperative networks
IEEE/ACM Transactions on Networking (TON)
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Selfish traffic allocation for server farms
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
How unfair is optimal routing?
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Queue Spillovers in Transportation Networks with a Route Choice
Transportation Science
How much can taxes help selfish routing?
Proceedings of the 4th ACM conference on Electronic commerce
Near-optimal network design with selfish agents
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Pricing network edges for heterogeneous selfish users
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Proceedings of the twenty-second annual symposium on Principles of distributed computing
The price of anarchy is independent of the network topology
Journal of Computer and System Sciences - STOC 2002
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
The maximum latency of selfish routing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Selfish Routing in Capacitated Networks
Mathematics of Operations Research
Selfish Routing and the Price of Anarchy
Selfish Routing and the Price of Anarchy
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Braess's paradox, fibonacci numbers, and exponential inapproximability
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands
Operations Research Letters
Altruism, selfishness, and spite in traffic routing
Proceedings of the 9th ACM conference on Electronic commerce
Sensitivity of Wardrop Equilibria
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Efficient coordination mechanisms for unrelated machine scheduling
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Stackelberg Routing in Arbitrary Networks
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Stabilization of the minimum latency flow in Braess graphs by state-dependent tax
Proceedings of the 3rd International Conference on Bio-Inspired Models of Network, Information and Computing Sytems
Efficient Methods for Selfish Network Design
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Eliciting Coordination with Rebates
Transportation Science
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Depletable channels: dynamics and behaviour
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Stackelberg Routing in Arbitrary Networks
Mathematics of Operations Research
Braess's paradox for flows over time
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Braess's paradox in large sparse graphs
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Selfish Traffic Allocation for Server Farms
SIAM Journal on Computing
Road traffic optimisation using an evolutionary game
Proceedings of the 13th annual conference companion on Genetic and evolutionary computation
Optimal sub-networks in traffic assignment problem and the Braess paradox
Computers and Industrial Engineering
Efficiency of restricted tolls in non-atomic network routing games
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
Selfish splittable flows and NP-completeness
Computer Science Review
Efficient methods for selfish network design
Theoretical Computer Science
Stronger Bounds on Braess's Paradox and the Maximum Latency of Selfish Routing
SIAM Journal on Discrete Mathematics
Random Structures & Algorithms
Finding pure nash equilibrium of graphical game via constraints satisfaction approach
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
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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We consider a directed network in which every edge possesses a latency function that specifies the time needed to traverse the edge given its congestion. Selfish, noncooperative agents constitute the network traffic and wish to travel from a source vertex s to a destination t as quickly as possible. Since the route chosen by one network user affects the congestion experienced by others, we model the problem as a noncooperative game. Assuming that 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.A natural measure for the performance of a network used by selfish agents is the common latency experienced by users in a Nash equilibrium. Braess's Paradox is the counterintuitive but well-known fact that removing edges from a network can improve its performance. Braess's Paradox motivates the following network design problem: given a network, which edges should be removed to obtain the best flow at Nash equilibrium? Equivalently, given a network of edges that can be built, which subnetwork will exhibit the best performance when used selfishly?We give optimal inapproximability results and approximation algorithms for this network design problem. For example, we prove that there is no approximation algorithm for this problem with approximation ratio less than n/2, where n is the number of network vertices, unless P = NP. We further show that this hardness result is the best possible, by exhibiting an (n/2)-approximation algorithm. We also prove tight inapproximability results when additional structure, such as linearity, is imposed on the network latency functions.Moreover, we prove that an optimal approximation algorithm for these problems is the trivial algorithm: given a network of candidate edges, build the entire network. As a consequence, we show that Braess's Paradox--even in its worst-possible manifestations--is impossible to detect efficiently.En route to these results, we give a fundamental generalization of Braess's Paradox: the improvement in performance that can be effected by removing edges can be arbitrarily large in large networks. Even though Braess's Paradox has enjoyed 35 years as a textbook example, our result is the first to extend its severity beyond that in Braess's original four-node network.