Inefficiency of Nash equilibria
Mathematics of Operations Research
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
Selfish traffic allocation for server farms
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The price of anarchy is independent of the network topology
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Designing Networks for Selfish Users is Hard
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
The maximum latency of selfish routing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The Price of Routing Unsplittable Flow
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The price of anarchy of finite congestion games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Taxes for linear atomic congestion games
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Efficient Methods for Selfish Network Design
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
The hardness of selective network design for bottleneck routing games
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Taxes for linear atomic congestion games
ACM Transactions on Algorithms (TALG)
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
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In this paper we consider the network design for selfish users problem, where we assume the more realistic unsplittable model in which the users can have general demands and each user must choose a single path between its source and its destination. This model is also called atomic (weighted) network congestion game. The problem can be presented as follows : given a network, which edges should be removed to minimize the cost of the worst Nash equilibrium? We consider both computational issues and existential issues (i.e. the power of network design). We give inapproximability results and approximation algorithms for this network design problem. For networks with linear edge latency functions we prove that there is no approximation algorithm for this problem with approximation ratio less then $(3+\sqrt{5})/2 \approx 2.618$ unless P=NP. We also show that for networks with polynomials of degree d edge latency functions there is no approximation algorithm for this problem with approximation ratio less then $d^{{\it \Theta}(d)}$ unless P=NP. Moreover, we observe that the trivial algorithm that builds the entire network is optimal for linear edge latency functions and has an approximation ratio of $d^{{\it \Theta}(d)}$ for polynomials of degree d edge latency functions. Finally, we consider general continuous, non-decreasing edge latency functions and show that the approximation ratio of any approximation algorithm for this problem is unbounded, assuming P ≠ NP. In terms of existential issues we show that network design cannot improve the maximum possible bound on the price of anarchy in the worst case. Previous results of Roughgarden for networks with n vertices where each user controls only a negligible fraction of the overall traffic showed optimal inapproximability results of 4/3 for linear edge latency functions, ${\it \Theta}(d /{\rm ln} d)$ for polynomial edge latency functions and n/2 for general continuous non-decreasing edge latency functions. He also showed that the trivial algorithm that builds the entire network is optimal for that case.