Randomized truthful mechanisms for scheduling unrelated machines

Abstract

In this paper, we consider randomized truthful mechanisms for scheduling tasks to unrelated machines, where each machine is controlled by a selfish agent. Some previous work on this topic focused on a special case, scheduling two machines, for which the best approximation ratio is 1.6737 [5] and the best lower bound is 1.5 [6]. For this case, we give a unified framework for designing universally truthful mechanisms, which includes all the known mechanisms, and also a tight analysis method of their approximation ratios. Based on this, we give an improved randomized truthful mechanism, whose approximation ratio is 1.5963. For the general case, when there are m machines, the only known technique is to obtain a -approximation truthful mechanism by generalizing a γ-approximation truthful mechanism for two machines[6]. There is a barrier of 0.75m for this technique due to the lower bound of 1.5 for two machines. We break this 0.75m barrier by a new designing technique, rounding a fractional solution. We propose a randomized truthful-in-expectation mechanism that achieves approximation of, for m machines. For the lower bound side, we focus on an interesting family of mechanisms, namely task-independent truthful mechanisms. We prove a lower bound of 11/7 for two machines and a lower bound of for m machines with respect to this family. They almost match our upper bounds in both cases. © 2008 Springer Berlin Heidelberg.