The Nisan-Ronen conjecture states that no truthful mechanism for makespan-minimization when allocating $m$ tasks to $n$ unrelated machines can have approximation ratio less than $n$. Over more than two decades since its formulation, little progress has been made in resolving it and the best known lower bound is still a small constant. This work makes progress towards validating the conjecture by showing a lower bound of $1+\sqrt{n-1}$.

翻译：Nisan-Ronen的猜测指出,在将美元任务分配给非相关机器时,任何真实的机制都不能在将美元任务分配给非非相关机器时将美元任务最小化,其近似率不能低于n美元。 自制定以来的20多年中,在解决这一问题方面进展甚微,而最著名的下限仍是一个小的常态。 这项工作通过显示较低的1 {sqrt{n-1}美元约束度,在验证这一推测方面取得了进展。