When Stays Ahead Works Best

Stays ahead works well when:

$1.$ There is a natural measure of progress (end time, count, position..)

$2.$ Greedy's progress is easy to compare with any alternative's progress

$3.$ Being ahead at step $k$ helps you stay ahead at step $k+1$

$4.$ The inductive step is simple For activity selection, end time is a perfect measure. Finishing earlier gives more room for future activities. The induction flows naturally. If the comparison between greedy and others is direct, stays ahead is your tool.