In the allocation problem, asynchronous processors must partition a set of items so that each processor leave 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 power 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.