Tighter bounds on a heuristic for a partition problem
Information Processing Letters
Approximation schemes for scheduling
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Record Allocation for Minimizing Expected Retrieval Costs on Drum-Like Storage Devices
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
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
The maximum latency of selfish routing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Computing Nash equilibria for scheduling on restricted parallel links
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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
Selfish Routing and the Price of Anarchy
Selfish Routing and the Price of Anarchy
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Structure and complexity of extreme Nash equilibria
Theoretical Computer Science - Game theory meets theoretical computer science
Tradeoffs in worst-case equilibria
Theoretical Computer Science - Approximation and online algorithms
Tight bounds for worst-case equilibria
ACM Transactions on Algorithms (TALG)
The price of anarchy for polynomial social cost
Theoretical Computer Science
Convergence time to Nash equilibrium in load balancing
ACM Transactions on Algorithms (TALG)
Algorithmica
Nash equilibria in discrete routing games with convex latency functions
Journal of Computer and System Sciences
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Nash equilibria, the price of anarchy and the fully mixed nash equilibrium conjecture
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Atomic routing games on maximum congestion
Theoretical Computer Science
Mediated Equilibria in Load-Balancing Games
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Taxes for linear atomic congestion games
ACM Transactions on Algorithms (TALG)
Weighted congestion games: price of anarchy, universal worst-case examples, and tightness
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
The impact of altruism on the efficiency of atomic congestion games
TGC'10 Proceedings of the 5th international conference on Trustworthly global computing
Bottleneck congestion games with logarithmic price of anarchy
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Exact Price of Anarchy for Polynomial Congestion Games
SIAM Journal on Computing
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
The robust price of anarchy of altruistic games
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Efficiency analysis of load balancing games with and without activation costs
Journal of Scheduling
Hi-index | 5.23 |
In this work, we introduce and study a new, potentially rich model for selfish routing over non-cooperative networks, as an interesting hybridization of the two prevailing such models, namely the KPmodel [E. Koutsoupias, C.H. Papadimitriou, Worst-case equilibria, in: G. Meinel, S. Tison (Eds.), Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science, in: Lecture Notes in Computer Science, vol. 1563, Springer-Verlag, 1999, pp. 404-413] and the Wmodel [J.G. Wardrop, Some theoretical aspects of road traffic research, Proceedings of the of the Institute of Civil Engineers 1 (Pt. II) (1952) 325-378]. In the hybrid model, each of nusers is using a mixed strategy to ship its unsplittable traffic over a network consisting of m parallel links. In a Nash equilibrium, no user can unilaterally improve its Expected Individual Cost. To evaluate Nash equilibria, we introduce Quadratic Social Cost as the sum of the expectations of the latencies, incurred by the squares of the accumulated traffic. This modeling is unlike the KP model, where Social Cost [E. Koutsoupias, C.H. Papadimitriou, Worst-case equilibria, in: G. Meinel, S. Tison (Eds.), Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science, in: Lecture Notes in Computer Science, vol. 1563, Springer-Verlag, 1999, pp. 404-413] is the expectation of the maximum latency incurred by the accumulated traffic; but it is like the W model since the Quadratic Social Cost can be expressed as a weighted sum of Expected Individual Costs. We use the Quadratic Social Cost to define Quadratic Coordination Ratio. Here are our main findings: *Quadratic Social Cost can be computed in polynomial time. This is unlike the #P-completeness [D. Fotakis, S. Kontogiannis, E. Koutsoupias, M. Mavronicolas, P. Spirakis, The structure and complexity of Nash equilibria for a selfish routing game, in: P. Widmayer, F. Triguero, R. Morales, M. Hennessy, S. Eidenbenz, R. Conejo (Eds.), Proceedings of the 29th International Colloquium on Automata, Languages and Programming, in: Lecture Notes in Computer Science, vol. 2380, Springer-Verlag, 2002, pp. 123-134] of computing Social Cost for the KP model. *For the case of identical users and identical links, the fully mixed Nash equilibrium [M. Mavronicolas, P. Spirakis, The price of selfish routing, Algorithmica 48 (1) (2007) 91-126], where each user assigns positive probability to every link, maximizes Quadratic Social Cost. *As our main result, we present a comprehensive collection of tight, constant (that is, independent of m and n), strictly less than 2, lower and upper bounds on the Quadratic Coordination Ratio for several, interesting special cases. Some of the bounds stand in contrast to corresponding super-constant bounds on the Coordination Ratio previously shown in [A. Czumaj, B. Vocking, Tight bounds for worst-case equilibria, ACM Transactions on Algorithms 3 (1) (2007); E. Koutsoupias, M. Mavronicolas, P. Spirakis, Approximate equilibria and ball fusion, Theory of Computing Systems 36 (6) (2003) 683-693; E. Koutsoupias, C.H. Papadimitriou, Worst-case equilibria, in: G. Meinel, S. Tison (Eds.), Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science, in: Lecture Notes in Computer Science, vol. 1563, Springer-Verlag, 1999, pp. 404-413; M. Mavronicolas, P. Spirakis, The price of selfish routing, Algorithmica 48 (1) (2007) 91-126] for the KP model.