An On-Line Algorithm for Some Uniform Processor Scheduling
SIAM Journal on Computing
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
Journal of the ACM (JACM)
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
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
Selfish Routing and the Price of Anarchy
Selfish Routing and the Price of Anarchy
Tight bounds for worst-case equilibria
ACM Transactions on Algorithms (TALG)
Performance Guarantees of Local Search for Multiprocessor Scheduling
INFORMS Journal on Computing
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Convergence time to Nash equilibria
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Nashification and the coordination ratio for a selfish routing game
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
Strong and correlated strong equilibria in monotone congestion games
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Tighter approximation bounds for LPT scheduling in two special cases
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Strong price of anarchy for machine load balancing
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Selfish Scheduling with Setup Times
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
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Recent interest in Nash equilibria led to a study of the price of anarchy(poa) and the strong price of anarchy(spoa) for scheduling problems. The two measures express the worst case ratio between the cost of an equilibrium (a pure Nash equilibrium, and a strong equilibrium, respectively) to the cost of a social optimum.We consider scheduling on uniformly related machines. Here the atomic players are the jobs, and the delay of a job is the completion time of the machine running it, also called the load of this machine. The social goal is to minimize the maximum delay of any job, while the selfish goal of each job is to minimize its own delay, that is, the delay of the machine running it.While previous studies either consider identical speed machines or an arbitrary number of speeds, focusing on the number of machines as a parameter, we consider the situation in which the number of different speeds is small. We reveal a linear dependence between the number of speeds and the poa. For a set of machines of at most pspeeds, the poaturns out to be exactly p+ 1. The growth of the poafor large numbers of related machines is therefore a direct result of the large number of potential speeds. We further consider a well known structure of processors, where all machines are of the same speed except for one possibly faster machine. We investigate the poaas a function of both the speed of the fastest machine and the number of slow machines, and give tight bounds for nearly all cases.