Randomized Truthful Mechanisms for Scheduling Unrelated Machines

In this paper, we consider randomized truthful mechanisms for scheduling tasks to unrelated machines. each machine is controlled by a selfish agent. Some previous work oil this topic focused oil a, special case, scheduling two machines, for which the hest 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 all improved randomized truthful mechanism, whose approximation ratio is 1.5963. For the general case, when there, are in machines. the only known technique is to obtain it gamma m/2-approximation truthful mechanism by 2 generalizing it gamma-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 mechanism that achieves approximation of m + 5/2, for m machines. For the lower bound side. we focus oil an interesting family of mechanisms, namely truthful mechanisms. We prove a lower bound of 11/7 for two machines and a lower bound of m + 1/2 for m machines with respect to this family. They almost match our upper bounds in both cases.