ags@pucc-i (Seaman) (06/05/84)
My face is red! Last night I posted a method for round-robin scheduling
which involved using a backtracking program to find the appropriate first-
round pairings, plus a simple rotation to get the subsequent rounds. The
method was correct, but unnecessarily complicated. I have cancelled the
article, but it already had a pretty good head start.
After sleeping on the problem, I remembered something I knew 30 years ago:
the first-round pairings don't matter! Here is how it works, with example
for N=22:
1) If you have an odd number of participants, add one called "BYE" to make
it even.
2) Pair them off for the first round:
1 2 3 4 5 6 7 8 9 10 11
22 21 20 19 18 17 16 15 14 13 12
3) Hold one entry fixed (I'll use #22) and let the others rotate for
subsequent rounds. Second round is:
2 3 4 5 6 7 8 9 10 11 12
22 1 21 20 19 18 17 16 15 14 13
and so on.
Throwing away my backtracking program,
--
Dave Seaman
..!pur-ee!pucc-i:ags
"Against people who give vent to their loquacity
by extraneous bombastic circumlocution."