[EM] Beatpath Magnitude Algorithm Revision

MIKE OSSIPOFF nkklrp at hotmail.com
Mon Feb 5 13:14:32 PST 2001

It's occurred to me that the beatpath magnitude algorithm that I
sent would, during each pass, look at some or all of the permutations
of 3 candidates, taken from the entire set of candidates, more than
once. So maybe it would be better to just explicitly take each
3-candidate permutation from among all the candidates, for each

1. Have a 2-dimensional array of a variable I'll call xy.
2. If x beats y, then xy is equal to the magnitude of x's defeat of y.
   If x doesn't beat y, then xy = 0.
3. For each 3-candidate permutation, x,y,z, taken from the whole
   set of candidates, if min(xy,yz) > xz, then assign min(xy,yz)
   as the value of xz.
4. Repeat #3 till that repetition doesn't change any of the xy.

As I said, that's an amateur algorithm, and no doubt others on
this list could write, or have written more efficient ones.

It produces an array of beatpaths magnitudes, for use with
BeatpathWinner, or for determining the Schwartz set for SSD
or Cloneproof SSD.

I'd be interested if anyone could post faster algorithms for
obtaining an array of beatpath magnitudes, or for determining
the Schwartz set via some other approach.

Mike Ossipoff

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