Well not exactly because it’s the log of the number. So it’s log 1000 vs log 1000000 which is a much smaller difference. Also if you actually know the minimum

Well not exactly because it’s the log of the number. So it’s log 1000 vs log 1000000 which is a much smaller difference. Also if you actually know the minimum item it’s much better for it to be first because it means you can skip almost all the work. The paper is focused on doing the best for a worst case input. In real life if you can guess you can improve the average case substantially. For example, this is what A* tries to do.