A players and B players

[xman15]

I have a tourrnament with 8 A players and 8 B players.
In each round, each of the four games teams an A player with a B player vs. an A player and B player.
I would like to minimize the number of times you play with or against the same players, with 7 or 8 rounds.

[Ian Wakeling]

This is a similar problem to that of a mixed doubles competition.  There are standard schedules called spouse avoiding mixed doubles tournaments where you parnter and oppose everyone except your spouse exactly once.

(H1 W4 v H2 W7) (H3 W1 v H4 W5) (H5 W3 v H6 W8) (H7 W6 v H8 W2)
(H1 W7 v H3 W6) (H2 W5 v H7 W3) (H4 W2 v H5 W8) (H6 W1 v H8 W4)
(H1 W6 v H4 W8) (H2 W4 v H8 W5) (H3 W7 v H5 W2) (H6 W3 v H7 W1)
(H1 W3 v H5 W4) (H2 W8 v H6 W7) (H3 W5 v H8 W6) (H4 W1 v H7 W2)
(H1 W5 v H6 W2) (H2 W1 v H3 W8) (H4 W3 v H8 W7) (H5 W6 v H7 W4)
(H1 W8 v H7 W5) (H2 W3 v H4 W6) (H3 W2 v H6 W4) (H5 W7 v H8 W1)
(H1 W2 v H8 W3) (H2 W6 v H5 W1) (H3 W4 v H7 W8) (H4 W7 v H6 W5)

So I think the above gives you an option for 7 rounds of play, and you could play something like:

(H1 W1 v H2 W2) (H3 W3 v H4 W4) (H5 W5 v H6 W6) (H7 W7 v H8 W8)

if you wanted an eighth round.

[schedulecc]

This is almost perfect for my mixed doubles scenario, but is there a schedule that does 8 rounds on four courts that does have everyone pair with and play against all players (no spouse avoidance)?

[schedulecc]

Sorry, ignore the request.  I had mis-entered the schedule, it is perfect for 8 rounds.  This site is AWESOME, thank you so much!!

[dwfortner]

Hey, did you ever come up with an 8-week schedule for the mixed doubles that is not spouse avoiding?
I found a table for 16 players (8 women 8 men) in the paper Ian Co-wrote about generalizing the Spouse avoiding and strict mitchell mixed doubles round robin.
It shows a table for strict Mitchell Mixed Doubles Round Robin (strict MMDRR( 8 ) ), which has been really helpful, but I would love to know if someone worked through what an 8-round schedule of those matches would look like, with all players playing each round, if that's even possible.

[Ian Wakeling]

Hi, thanks for looking at the paper.  My best guess is that the schedule you want does not exist.  What I know is that the construction shown in the paper for larger schedules of 20, 24, 28,... players does not work for 16, and I have tried without any success to find a 16 player schedule by computer search. It is possible to have 16 players in 11 rounds on 3 courts (example 2.11), but of course there will be people with byes in every round.

[dwfortner]

Thanks for the feed back. I figured there was no solution for the 8-round 4 court schedule. 
We've landed on a sort of hybrid schedule where there's a mix of multiple opponents. Similar to the Spouse avoidance with the additional round.
Thanks for the work you've done in the analysis and proof of all that. It's really hard to find stuff out there for these types of schedules.
To me that's surprising. I guess the way sports are going (pickleball, for example), it's more the case where you're either going to have a set partner or you're going to mix with everyone (so, like a 16-player whist) and most people don't care about actual mixed doubles.
Again, thanks for the work and feedback, and generally making yourself available. THis forum is really cool. Nice work