consider a graph modeling a project composed of a set of serializable, partially interdependent activities, where the activities are represented by edges and the interdependence by nodes such that 2 edges e1
, e2
are incident iff the e1
activity must be completed before the activity e2
can start. assume 2 special vertices s
,t
representing the start and the end of a project, resp.
in such a model, the critical path describes a maximal sequence of activities that cannot be parallelized wrt each other.
its name stems from the fact that any delay in precisely one of the activities on the critical path necessarily delays the complete project while for all other activities there is some buffer time available.
in particular the critical path does not necessarily match those activities which are essential for an overall success to the project.
the critical path corresponds to the longest path between s
, t
in the graph.
the critical path need not be unique, of course.