Dynamic-programming in the problem of optimization of a covering

The problem of allocating assignments to operators with possible redundancy of some assignments, as well as to its abstract analogue, meaning optimization of a measurable space covering, is considered. A modification of the dynamic programming procedure reduced to a ‘functional level’ algorithm has been constructed. This formulation appears, in particular, in studying the problem of several travelling salespersons, where optimization in the class of coverings may turn out to be important at the ‘distributive’ level.