What's funny is just how simple these algorithms are. All it really took was something looking at this from a slightly different perspective.
The best optimizations I've done at my job have been exactly that. Looking at things a little differently and even removing steps. It's really a testament to open-mindedness and creativity.
Here is my favourite elevator optimisation story [1]. Customers were complaining that the lifts were taking too long to arrive. It turned out the root problem was boredom, and the solution was to install mirrors in the lobby. The mirrors allowed people to fill in the time by admiring themselves and others. A neat illustration of how there are sometimes simple non-engineering solutions!
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Update: Q: Have I been suckered by an urban myth here? I have a vague recollection of knowing this story before the publication date of the source I gave, and it seems to be well used in "management" books but no mention of specifics or a primary source.
Further poking around comes up with an article that claims the story originates with a consultant friend of Russell Ackoff (the author of the book I linked to), and took place in a New York hotel in 1955. A bit more specific, but I'm still a bit suspect since Ackoff doesn't seem to mention these details in his writing. Presumably if it is mentioned in the earlier book that you point to, Ackoff must have published or mentioned it elsewhere. I've done this one to death now, so I think I'll move on.
Basically some problems are made trivially easy, without having to change the problem definition by changing the underlying representation of the problem.
The best optimizations I've done at my job have been exactly that. Looking at things a little differently and even removing steps. It's really a testament to open-mindedness and creativity.