We study the scheduling problem on unrelated machines in the mechanism design
setting. This problem was proposed and studied in the seminal paper (Nisan and
Ronen 1999), where they gave a 1.75-approximation randomized truthful mechanism
for the case of two machines. We improve this result by a 1.6737-approximation
randomized truthful mechanism. We also generalize our result to a
0.8368m-approximation mechanism for task scheduling with m machines, which
improve the previous best upper bound of $0.875m(Mu'alem and Schapira 2007)
