Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
(Almost) optimal coordination mechanisms for unrelated machine scheduling
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient coordination mechanisms for unrelated machine scheduling
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Coordination mechanisms for selfish scheduling
Theoretical Computer Science
Inner product spaces for MinSum coordination mechanisms
Proceedings of the forty-third annual ACM symposium on Theory of computing
Non-clairvoyant Scheduling Games
Theory of Computing Systems - Special Issue: Algorithmic Game Theory
Computer Science Review
Smooth inequalities and equilibrium inefficiency in scheduling games
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
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We investigate coordination mechanisms that schedule n jobs on m unrelated machines. The objective is to minimize the latest completion of all jobs, i.e., the makespan. It is known that if the mechanism is non-preemptive, the price of anarchy is Ω(logm). Both Azar, Jain, and Mirrokni (SODA 2008) and Caragiannis (SODA 2009) raised the question whether it is possible to design a coordination mechanism that has constant price of anarchy using preemption. We give a negative answer. All deterministic coordination mechanisms, if they are symmetric and satisfy the property of independence of irrelevant alternatives, even with preemption, have the price of anarchy $\Omega(\frac{\log m}{\log \log m})$. Moreover, all randomized coordination mechanisms, if they are symmetric and unbiased, even with preemption, have similarly the price of anarchy $\Omega(\frac{\log m}{\log \log m})$. Our lower bound complements the result of Caragiannis, whose bcoord mechanism guarantees $O(\frac{\log m}{\log \log m})$ price of anarchy. Our lower bound construction is surprisingly simple. En route we prove a Ramsey-type graph theorem, which can be of independent interest. On the positive side, we observe that our lower bound construction critically uses the fact that the inefficiency of a job on a machine can be unbounded. If, on the other hand, the inefficiency is not unbounded, we demonstrate that it is possible to break the $\Omega(\frac{\log m}{\log \log m})$ barrier on the price of anarchy by using known coordination mechanisms.