As you can see from our general remarks about decomposing problems, one way of decomposing a given problem is to find an activity (or a set of activities) that plays the same role that activity number 8 played in the previous chapter--the one that other activities necessarily precede or follow. Such an activity is known as a critical activity, and there is, in fact, a mathematical technique for identifying critical activities in a schedule. The technique is known as computing the transitive closure of the precedence relation imposed on the activities.

To put the same idea more formally, given a set of activities to schedule, we can identify an activity A such that any other activity B is either constrained to execute before A or constrained to execute after A by computing the transitive closure of the precedence relation.

This corresponds to the notion of "ranked activity" on Schedule Precedence Graphs.