In the allocation problem, asynchronous processors must partition a set of items so that each processor leaves knowing all items exclusively allocated to it. We introduce a new variant of the allocation problem called the assignment problem, in which processors might leave having only partial knowledge of their assigned items. The missing items in a processor's assignment must eventually be announced by other processors.

While allocation has consensus number 2, we show that the assignment problem is solvable read-write wait-free when k processors compete for at least $2k-1$ items. Moreover, we propose a long-lived read-write wait-free assignment algorithm which is fair, allocating no more than 2 items per processor, and in which a slow processor may delay the assignment of at most n items, where n is the number of processors.

The assignment problem and its read-write solution may be of practical interest for implementing resource allocators and work queues, which are pervasive concurrent programming patterns, as well as stream-processing systems.

在分配问题中，异步处理器必须对一组项目进行分区，以便每个处理器都知道专门分配给它的所有项目。我们引入了分配问题的一个新变体，称为分配问题，其中处理器可能只知道他们分配的项目的部分知识。处理器分配中丢失的项目最终必须由其他处理器宣布。

虽然分配的共识编号为 2，但我们表明，当k 个处理器至少竞争时，分配问题是可解决的读写等待$2克-1$项目。此外，我们提出了一种长寿命的读写无等待分配算法，它是公平的，每个处理器分配不超过 2 个项目，其中一个慢速处理器可能会延迟最多n 个项目的分配，其中n是数量处理器。

分配问题及其读写解决方案可能对实现资源分配器和工作队列具有实际意义，它们是普遍存在的并发编程模式以及流处理系统。