A Deterministic Truthful PTAS for Scheduling Related Machines

Scheduling on related machines ($Q||C_{\max}$) is one of the most important problems in the field of algorithmic mechanism design. Each machine is controlled by a selfish agent and her valuation function can be expressed via a single parameter, her speed. Archer and Tardos [Proceedings of the 42nd Annual Symposium on Foundations of Computer Science (FOCS), Las Vegas, NV, 2001, pp. 482--491] showed that, in contrast to other similar problems, a (nonpolynomial) allocation that minimizes the makespan can be truthfully implemented. On the other hand, if we leave out the game-theoretic issues, the complexity of the problem has been completely settled---the problem is strongly NP-hard, while there exists a polynomial-time approximation scheme (PTAS) [D. S. Hochbaum and D. B. Shmoys, SIAM J. Comput., 17 (1988), pp. 539--551, and L. Epstein and J. Sgall, Algorithmica, 39(1) (2004), pp. 43--57]. This problem is the most well studied in single-parameter algorithmic mechanism design. It gives an excellent ground to ...

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