Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
The competitiveness of on-line assignments
Journal of Algorithms
Achieving network optima using Stackelberg routing strategies
IEEE/ACM Transactions on Networking (TON)
On-line routing of virtual circuits with applications to load balancing and machine scheduling
Journal of the ACM (JACM)
Heuristic Algorithms for Scheduling Independent Tasks on Nonidentical Processors
Journal of the ACM (JACM)
Algorithms for Scheduling Tasks on Unrelated Processors
Journal of the ACM (JACM)
Stackelberg scheduling strategies
STOC '01 Proceedings of the thirty-third 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
(Incremental) priority algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
How much can taxes help selfish routing?
Proceedings of the 4th ACM conference on Electronic commerce
Computing Nash equilibria for scheduling on restricted parallel links
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Tolls for Heterogeneous Selfish Users in Multicommodity Networks and Generalized Congestion Games
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Sink Equilibria and Convergence
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Convergence time to Nash equilibria
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Coordination mechanisms for selfish scheduling
WINE'05 Proceedings of the First international conference on Internet and Network Economics
Non-preemptive Coordination Mechanisms for Identical Machine Scheduling Games
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Efficient coordination mechanisms for unrelated machine scheduling
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Worst-Case Nash Equilibria in Restricted Routing
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Coordination mechanisms for selfish scheduling
Theoretical Computer Science
Theoretical Computer Science
Non-clairvoyant Scheduling Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Covering Games: Approximation through Non-cooperation
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Selfish Scheduling with Setup Times
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Stability and Convergence in Selfish Scheduling with Altruistic Agents
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Price of anarchy in parallel processing
Information Processing Letters
Mechanism Design for Decentralized Online Machine Scheduling
Operations Research
Inner product spaces for MinSum coordination mechanisms
Proceedings of the forty-third annual ACM symposium on Theory of computing
Improving the price of anarchy for selfish routing via coordination mechanisms
ESA'11 Proceedings of the 19th European conference on Algorithms
Dynamic inefficiency: anarchy without stability
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
The price of anarchy for minsum related machine scheduling
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Coordination mechanisms for selfish parallel jobs scheduling
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Preemptive coordination mechanisms for unrelated machines
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Smooth inequalities and equilibrium inefficiency in scheduling games
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Coordination mechanism for selfish scheduling under a grade of service provision
Information Processing Letters
NP-hardness of pure Nash equilibrium in Scheduling and Network Design Games
Theoretical Computer Science
Inefficiency of Nash equilibria with parallel processing policy
Information Processing Letters
Coordination mechanisms from (almost) all scheduling policies
Proceedings of the 5th conference on Innovations in theoretical computer science
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We investigate the influence of different algorithmic choices on the approximation ratio in selfish scheduling. Our goal is to design local policies that minimize the inefficiency of resulting equilibria. In particular, we design optimal coordination mechanisms for unrelated machine scheduling, and improve the known approximation ratio from Θ(m) to Θ(log m), where m is the number of machines. A local policy for each machine orders the set of jobs assigned to it only based on parameters of those jobs. A strongly local policy only uses the processing time of jobs on the the same machine. We prove that the approximation ratio of any set of strongly local ordering policies in equilibria is at least Ω(m). In particular, it implies that the approximation ratio of a greedy shortest-first algorithm for machine scheduling is at least Ω(m). This closes the gap between the known lower and upper bounds for this problem, and answers an open question raised by Ibarra and Kim [16], and Davis and Jaffe [10]. We then design a local ordering policy with the approximation ratio of Θ(log m) in equilibria, and prove that this policy is optimal among all local ordering policies. This policy orders the jobs in the non-decreasing order of their inefficiency, i.e, the ratio between the processing time on that machine over the minimum processing time. Finally, we show that best responses of players for the inefficiency-based policy may not converge to a pure Nash equilibrium, and present a Θ(log2 m) policy for which we can prove fast convergence of best responses to pure Nash equilibria.