You have one processor and n jobs. Each job requires time t_i. You want to minimize the average completion time.
Greedy Strategy?
Shortest Job First.
Process jobs in increasing order of length.
This minimizes the waiting time for subsequent jobs.
Can we use Greedy to find the Maximum Independent Set on a general graph?
No.
This is NP-Hard for general graphs. Greedy heuristics (like pick min-degree node) can fail.
However, for Trees, a greedy approach (process leaves up) works.