Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Near-optimal network design with selfish agents
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Designing Networks for Selfish Users is Hard
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
The price of anarchy is independent of the network topology
Journal of Computer and System Sciences - STOC 2002
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
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
Efficiency Loss in a Network Resource Allocation Game
Mathematics of Operations Research
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
The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands
Operations Research Letters
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
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
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Altruism, selfishness, and spite in traffic routing
Proceedings of the 9th ACM conference on Electronic commerce
Efficient Methods for Selfish Network Design
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Stackelberg Routing in Arbitrary Networks
Mathematics of Operations Research
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
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
Hi-index | 0.00 |
We give the first analyses in multicommodity networks of both the worst-case severity of Braess’s Paradox and the price of anarchy of selfish routing with respect to the maximum latency. Our first main result is a construction of an infinite family of two-commodity networks, related to the Fibonacci numbers, in which both of these quantities grow exponentially with the size of the network. This construction has wide implications, and demonstrates that numerous existing analyses of selfish routing in single-commodity networks have no analogues in multicommodity networks, even in those with only two commodities. This dichotomy between single- and two-commodity networks is arguably quite unexpected, given the negligible dependence on the number of commodities of previous work on selfish routing. Our second main result is an exponential upper bound on the worst-possible severity of Braess’s Paradox and on the price of anarchy for the maximum latency, which essentially matches the lower bound when the number of commodities is constant. Finally, we use our family of two-commodity networks to exhibit a natural network design problem with intrinsically exponential (in)approximability: while there is a polynomial-time algorithm with an exponential approximation ratio, subexponential approximation is unachievable in polynomial time (assuming P ≠ NP).