Задача Штейнера для ацикдического графа

The Steiner problem for graph without cycles is considered in the paper. The algebraic approach is used for the problem investigation and solution. The operations under simple chains sets are introduced and the properties of this operations are considered. The notions of completeness, base, canonic base for simple chains sets are defined. It is offered a simple algorithm for problem solution which uses previously defined base chains. It is shown the polynomial complexity of the problem.