Renaming is a task in distributed computing where $n$ processes are assigned new names from a name space of size $m$. The problem is called tight if $m=n$, and loose if $m>n$. In recent years renaming came to the fore again and new algorithms were developed. For tight renaming in asynchronous shared memory systems, Alistarh et al. describe a construction based on the AKS network that assigns all names within $\mathcal{O}(logn)$ steps per process. They also show that, depending on the size of the name space, loose renaming can be done considerably faster. For $m=(1+ϵ)\cdot n$ and constant $ϵ$, they achieve a step complexity of $\mathcal{O}(loglogn)$.

In this paper we consider tight as well as loose renaming and introduce randomized algorithms that achieve their tasks with high probability. The model assumed is the asynchronous shared-memory model against an adaptive adversary. Our algorithm for loose renaming maps $n$ processes to a name space of size $m=(1+2∕{(logn)}^{\ell })\cdot n=(1+o\left(1\right))\cdot n$ performing $\mathcal{O}\left(\ell \cdot {(loglogn)}^2\right)$ test-and-set operations. In the case of tight renaming, we present a protocol that assigns $n$ processes to $n$ names with step complexity $\mathcal{O}(logn)$, but without the overhead and impracticality of the AKS network. This algorithm utilizes modern hardware features in form of a counting device which is also described in the paper. This device may have the potential to speed up other distributed algorithms as well.

重命名是分布式计算中的一项任务，其中 $ñ$ 从大小大小的名称空间为进程分配新名称 $米$。这个问题被称为紧，如果$米=ñ$和松散的，如果$米>ñ$。近年来，重命名再次崭露头角，并开发了新算法。对于异步共享内存系统中的重命名，Alistarh等人。描述基于AKS网络的结构，该结构在其中分配所有名称$\mathcal{Ø}（日志ñ）$每个过程的步骤。他们还表明，根据名称空间的大小，可以较快地进行宽松的重命名。对于$米=（\mathrm{1个}+ϵ）\cdot ñ$ 并且恒定 $ϵ$，它们的步复杂度为 $\mathcal{Ø}（日志日志ñ）$。

在本文中，我们考虑了重命名以及宽松的重命名，并介绍了以高概率实现其任务的随机算法。假定的模型是针对自适应对手的异步共享内存模型。我们的宽松地图重命名算法$ñ$ 处理到大小为一定的名称空间 $米=（\mathrm{1个}+2∕{（日志ñ）}^{\ell }）\cdot ñ=（\mathrm{1个}+Ø（\mathrm{1个}））\cdot ñ$ 表演 $\mathcal{Ø}（\ell \cdot {（日志日志ñ）}^2）$测试和设置操作。在重命名的情况下，我们提出一个分配$ñ$ 过程 $ñ$ 具有步骤复杂性的名称 $\mathcal{Ø}（日志ñ）$，但没有AKS网络的开销和不切实际。该算法利用计数设备形式的现代硬件功能，该功能也在本文中进行了描述。该设备也可能具有加速其他分布式算法的潜力。