Combinatorics in operations research
Handbook of combinatorics (vol. 2)
P-Complete Approximation Problems
Journal of the ACM (JACM)
Sharing the cost of multicast transmissions
Journal of Computer and System Sciences - Special issue on Internet algorithms
Load balancing in the L/sub p/ norm
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Expressive negotiation over donations to charities
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
Fairness and optimality in congestion games
Proceedings of the 6th ACM conference on Electronic commerce
Selfish Routing and the Price of Anarchy
Selfish Routing and the Price of Anarchy
Welfare maximization in congestion games
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Algorithmic Game Theory
Expressive negotiation in settings with externalities
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
The Price of Stability for Network Design with Fair Cost Allocation
SIAM Journal on Computing
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We consider a variant of congestion games where every player i expresses for each resource e and player j a positive externality, i.e., a value for being on e together with player j. Rather than adopting a game-theoretic perspective, we take an optimization point of view and consider the problem of optimizing the social welfare. We show that this problem is NP-hard even for very special cases, notably also for the case where the players' utility functions for each resource are affine (contrasting with the tractable case of linear functions [3]). We derive a 2-approximation algorithm by rounding an optimal solution of a natural LP formulation of the problem. Our rounding procedure is sophisticated because it needs to take care of the dependencies between the players resulting from the pairwise externalities. We also show that this is essentially best possible by showing that the integrality gap of the LP is close to 2. Small adaptations of our rounding approach enable us to derive approximation algorithms for several generalizations of the problem. Most notably, we obtain an (r+1)-approximation when every player may express for each resource externalities on player sets of size r. Further, we derive a 2-approximation when the strategy sets of the players are restricted and a $\frac32$-approximation when these sets are of size 2.