[EM] Proof that Floyd's works in one pass?

[MIKE OSSIPOFF]

Yesterday I asked Russ, the website owner, to re-arrange the indices in the 
core of the strongest-beatpaths algorithm, the part that tests and 
re-assigns the B(i,j). But today I wrote again and suggested that he not 
make that change until I send him a proof that it will achieve its intended 
result. But, when I wrote today, I said that we shouldn't call it the Floyd 
algorithm. I said that we should delete that name from it. Not only because 
of the order of the indices, but also because the websites say that the 
Floyd algorithm is for finding shortest paths, and I don't know if it's 
still the Floyd algorithm when it's modified to find strongest beatpaths.

If it's true that the BeatpathWinner algorithm that I posted a few days ago 
would find the strongest beatpath between each ordered pair of candidates if 
the indices were re-arranged, then would someone post a proof of that? Or 
the URL of a website that has a proof?

Also, if there's another algorilthm that would also have a running-time of a 
lower order than my Beatpath algorithm, would someone post it here, 
jargon-free and plain, as my BeatpathWinner algorithm was posted here a few 
days ago? Or post the URL of a website that has such a description of such 
an algorithm?

Mike Ossipoff

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