We study the problem of truthfully scheduling m tasks to n selfish unrelated machines, under the objective of makespan minimization, as was introduced in the seminal work of Nisan and Ronen (in: The 31st Annual ACM symposium on Theory of Computing (STOC), 1999). Closing the current gap of [2.618, n] on the approximation ratio of deterministic truthful mechanisms is a notorious open problem in the field of algorithmic mechanism design. We provide the first such improvement in more than a decade, since the lower bounds of 2.414 (for \(n=3\)) and 2.618 (for \(n\rightarrow \infty\)) by Christodoulou et al. (in: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2007) and Koutsoupias and Vidali (in: Proceedings of Mathematical Foundations of Computer Science (MFCS), 2007), respectively. More specifically, we show that the currently best lower bound of 2.618 can be achieved even for just \(n=4\) machines; for \(n=5\) we already get the first improvement, namely 2.711; and allowing the number of machines to grow arbitrarily large we can get a lower bound of 2.755.

正如 Nisan 和 Ronen 的开创性工作中所介绍的那样，我们研究了将m 个任务真实地调度到n 个自私无关的机器上的问题，如 Nisan 和 Ronen 的开创性工作（在：第 31 届 ACM 计算理论研讨会（STOC），1999 年） ）。在确定性真实机制的近似率上缩小当前的差距 [2.618,  n ] 是算法机制设计领域臭名昭著的开放问题。我们提供了十多年来的第一个这样的改进，因为下限 2.414（对于\(n=3\)）和 2.618（对于\(n\rightarrow \infty\)) 由 Christodoulou 等人撰写。(in: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2007) and Koutsoupias and Vidali (in: Proceedings of Mathematical Foundations of Computer Science (MFCS), 2007)，分别。更具体地说，我们表明即使对于\(n=4\)机器，也可以实现当前最好的下限 2.618 ；对于\(n=5\)我们已经得到了第一个改进，即 2.711；允许机器数量任意增加，我们可以得到下限 2.755。