Warm Up – 3/27 - Thursday Write a priority list using the decreasing time algorithm. Do you see any problem with this?

Weaknesses of Decreasing Time A decreasing time algorithm does not take into account tasks that are necessary to begin other tasks.

Weaknesses of Decreasing Time In the graph below AF is the last prioritized of the first available options. But AF needs to get done in order to get to IF, which has to get done to get to IW, which has to get done to get to ID. In a sense AF halts all progress.

Critical Times Instead of just looking a time we need to value how much time comes after a given vertex in order to prioritize correctly. We use what is called the Backflow Algorithm to find the “critical time” for each vertex. The critical time is the highest total processing time from a vertex to the finish.

Example #1 To find the critical times we start at the end and work our way backwards, adding up the largest possible time to the end.

Example #1 The critical times are put in brackets. The critical time for the project is 34.