An Optimal Lower Bound for Anonymous Scheduling Mechanism

We consider the problem of designing truthful mechanisms to minimize the makespan onm unrelated machines. In their seminal paper, Nisan and Ronen [14] showed a lower bound of 2, and an upper bound of m, thus leaving a large gap. They conjectured that their upper bound is tight, but were unable to prove it. Despite many attempts that yield positive results for several special cases, the conjecture is far from being solved: the lower bound was only recently slightly increased to 2.61 [5, 10], while the best upper bound remained unchanged. In this paper we show the optimal lower bound on truthful anonymous mechanisms: no such mechanism can guarantee an approximation ratio better than m. This is the first concrete evidence to the correctness of the Nisan-Ronen conjecture, especially given that the classic scheduling algorithms are anonymous, and all state-of-the-art mechanisms for special cases of the problem are anonymous as well. ∗Harvard Business School, Harvard. Email: [email protected]. †The School of Computer Science and Engineering, the Hebrew University of Jerusalem. Supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities, and by a grant from the Israeli Academy of Sciences. Email: [email protected]. ‡IE&M, Technion. Supported by grants from the Israeli Science Foundation and the Binational Science Foundation. Email: [email protected].