1) Different sections of the hall get dirtier at different rates, so merely dividing the hall into fifths might not be the best use of time
2) The broom looses efficiency over time of drag. Dust is absorbed into the broom and not the pile, dust in the broom will more than likely be redistributed on the floor. Short bursts of brushing seems more effective than long drags.
3) The pattern of brushing also makes a difference. The kids tend to sweep parallel to the walls, but sweeping perpendicular to the walls seems to yield more dust in the piles, because you can better get into the molding, but to clean the whole hall using perpendicular strokes would be tedious and probably have a net loss of efficiency.
4) Re-sweeping is also a problem. The brooms are very efficient, if used in short controlled sweeps, so re-sweeping an area is a waste of energy.
5) Sweeping in one direction seems to be more efficient when combine with short sweeps, but then energy is wasted walking back to the starting position from the ending position. So is only sweeping in one position truly more efficient?
Currently I sweep perpendicular to the walls to bring the dust more into the center of the hall. Then I sweep parallel to the halls but only in one direction. This creates a line of dust at the place where I start and stop my sweeps. I then sweep perpendicular to the walls again bringing all my lines of grime into one concise pile. That is how I currently do things, but I have been thinking of some new algorithms that might be more efficient. Who knows, maybe I may get an Ig Noble Award if I work this all the way out. A boy can dream, a boy can dream…