[EM] Floyd Algorithm?

Markus Schulze markus.schulze at alumni.tu-berlin.de
Thu Dec 18 02:45:02 PST 2003

Dear Mike,

you wrote (17 Dec 2003):

> Wrong. I don't call that the Floyd algorithm.

You do. You call that the Floyd algorithm

> Determine "beatpath" magnitudes array using the Floyd Algorithm:
> Def[i,j] will be the maximum beatpath magnitudes array. The i,j
> entry is the greatest magnitude of any beatpath from i to j. A
> beatpath's magnitude is the magnitude of its weakest defeat.

But the then used algorithm is clearly not the Floyd algorithm

>    changing = 1
>    while changing:
>        changing = 0
>        for i in range(nc):
>            for j in range(nc):
>                for k in range(nc):
>                    dmin = min ( Def[i,j], Def[j,k] )
>                    if Def[i,k] < dmin:
>                        Def[i,k] = dmin
>                        changing = 1

The Floyd algorithm has a runtime O(N^3), where N is the number of
candidates. But what you call the "Floyd Algorithm" has a runtime


You wrote (17 Dec 2003):
> It's part of the algorithm that I send people for counting
> BeatpathWinner. I'll post that BeatpathWinner algorithm here
> in a few minutes.

A correct version of the Floyd algorithm can be found in my paper
"A New Monotonic and Clone-Independent Single-Winner Election Method":

Markus Schulze

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