Truthful Approximation Schemes for Single-Parameter Agents

We present the first monotone randomized polynomial-time approximation scheme (PTAS) for minimizing the makespan of parallel related machines (Q||C_max), the paradigmatic problem in single-parameter algorithmic mechanism design. This result immediately gives a polynomial-time, truthful (in expectation) mechanism whose approximation guarantee attains the best-possible one for all polynomial-time algorithms (assuming P not equal to NP). Our algorithmic techniques are flexible and also yield, among other results, a monotone deterministic quasi-PTAS for Q||C_max and a monotone randomized PTAS for max-min scheduling on related machines.