On 2-player randomized mechanisms for scheduling

Abstract

In this paper, we study randomized truthful mechanisms for scheduling unrelated machines. We focus on the case of scheduling two machines, which is also the focus of many previous works [12,13,6,4]. For this problem, [13] gave the current best mechanism with an approximation ratio of 1.5963 and [14] proved a lower bound of 1.5. In this work, we introduce a natural technical assumption called scale-free, which says that the allocation will not change if the instance is scaled by a global factor. Under this assumption, we prove a better lower bound of (=1.5625). We then study a further special case, namely scheduling two tasks on two machines. For this setting, we provide a correlation mechanism which has an approximation ratio of 1.5089. We also prove a lower bound of 1.506 for all the randomized scale-free truthful mechanisms in this setting. © 2009 Springer-Verlag Berlin Heidelberg.