
Bounds for Sorting by Prefix Reversal by William H. Gates (1979) [pdf] - dennisbest
http://www.cs.berkeley.edu/~christos/papers/Bounds%20For%20Sorting%20By%20Prefix%20Reversal.pdf
======
hendzen
Christos Papadimitriou was asked about this paper in a recent interview[0] -
his response is below:

\------------------------------------

When I was an assistant professor at Harvard, Bill was a junior. My girlfriend
back then said that I had told her: "There's this undergrad at school who is
the smartest person I've ever met."

That semester, Gates was fascinated with a math problem called pancake
sorting: How can you sort a list of numbers, say 3-4-2-1-5, by flipping
prefixes of the list? You can flip the first two numbers to get 4-3-2-1-5, and
the first four to finish it off: 1-2-3-4-5. Just two flips. But for a list of
n numbers, nobody knew how to do it with fewer than 2n flips. Bill came to me
with an idea for doing it with only 1.67n flips. We proved his algorithm
correct, and we proved a lower bound—it cannot be done faster than 1.06n
flips. We held the record in pancake sorting for decades. It was a silly
problem back then, but it became important, because human chromosomes mutate
this way.

Two years later, I called to tell him our paper had been accepted to a fine
math journal. He sounded eminently disinterested. He had moved to Albuquerque,
New Mexico to run a small company writing code for microprocessors, of all
things. I remember thinking: "Such a brilliant kid. What a waste."

[0] -
[http://awards.acm.org/info/papadimitriou_4558987.cfm](http://awards.acm.org/info/papadimitriou_4558987.cfm)

~~~
agumonkey
The previous formatting got me so confused, I thought `>` was a prefix swap
operator ...

Anyways, I'd never have thought Gates was so mathematically inclined before
starting Microsoft. Many times, articles about him in college were more about
how he peeked on others code found in the trash. It's a tiny bit of a waste,
but if he had kept doing proofs he would never have been the "historical"
figure that he is now.

------
taspeotis
Trivia: this was the most efficient known algorithm until 2008 [1].

> On September 17, 2008, a team of researchers at the University of Texas at
> Dallas led by Founders Professor Hal Sudborough announced the acceptance by
> the journal Theoretical Computer Science of a more efficient algorithm for
> pancake sorting than the one proposed by Bill Gates and Christos
> Papadimitriou. This establishes a new upper bound ... improving upon the
> existing bound ... from 1979.

[1]
[https://en.wikipedia.org/wiki/Pancake_sorting](https://en.wikipedia.org/wiki/Pancake_sorting)

------
pvg
...and Christos Papadimitriou (also not some random unknown slouch) -
[https://en.wikipedia.org/wiki/Christos_Papadimitriou](https://en.wikipedia.org/wiki/Christos_Papadimitriou)

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ap22213
Wow - the guy's simply amazing.

So, what would I do if I was as smart, rich, and old as billg? I'd invest in
things that exponentially accelerate the rate of collective Human scientific
and technological progress. Then, I'd sit back, relax, and wait for a cure for
old-age to appear...

------
aarestad
I appreciated how easy it was to read, at least until it got to the formal
proof. This might be a good interview question to pose - to ask the
interviewee to come up with the trivial lower and upper bounds of "pancake
flips".

