<i>"Would you believe me if I claimed that an algorithm that has been on the books as "optimal" for 46 years, which has been analyzed in excruciating detail by geniuses like Knuth and taught in all computer science courses in the world, can be optimized to run 10 times faster?"</i>
I think this is pretty much identical to the subject being discussed here:<p><a href="http://news.ycombinator.com/item?id=1426211" rel="nofollow">http://news.ycombinator.com/item?id=1426211</a><p>There's a lot of discussion there already, and it might be worth reading it before commenting here and repeating all the arguments.<p>ADDED IN EDIT: Having gone and taken my own advice (for a change 8-) I prefer the other article because the diagrams are larger and in-line.