Distribution of assignments among participants under conditions of constraints

The distribution problem of assignments among participants in the presence of constraints is considered. For each assignment participants are defined, whom this assignment can be transferred to, and participants who cannot take the given assignment. Some collections of assignments are marked as clusters, i.e., all assignments of each such cluster can be given up only to one participant; and clusters can be intersected. Estimates of the extremum are set out, an approximate algorithm of the solution is proposed. The problems of this type can be met with, for example, in multiprocessor computing complexes in the distribution of assignments among processors, in the distribution of jobs among executors, and in a number of other cases.