If we only know the value of the longest path, can we determine the critical events?
From the longest path value of 20 in →Fig. 2.70, we can observe that the longest path is v1v2v5v7. But this is only a result of observation. Only using the information from various points in this table, we cannot “calculate” the corresponding vertices for the critical events. We need further information to ascertain the characteristic data of the critical events.
We can try to deduce from the other direction. Using vertex v6 as an example, since the value of vertex v7 is 20, even if vertex v6 starts at 20–a10 = 14, the overall progress would not be impacted. Therefore, the starting moment of v6, 9, in →Fig. 2.70, is the earliest possible starting time. The moment 14 reverse deduction from the sink vertex is the latest possible starting time.
Let us look again at the latest starting time of vertex v5, 20 – a9 = 11. This moment is the same as its earliest starting time. Therefore, we can use reverse deduction to calculate the latest possible starting moments of all events, and then perform the analysis.