An algorithm for decomposition of a non-convex set of vertices of a directed graph

Equivalent transformations are analyzed of a directed loopless graph that simplify decomposition of a non-convex set of vertices into a minimal set of convex subsets. An algorithm is discussed which additionally minimizes the size of the associated section of the graph. The findings may be useful in analyzing the flowchart of informational inter-linkage of MIS tasks where the data stored externally has to be minimized.