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

[dwfortner]

Hey, I put together that schedule, I wanted to run it past my team to see if they liked the overall balance of it better (I do), and I did find one small error in that table showing the resolution for Example 2.11:
In the 6th row, columns 4 and 5, it works out if those are switched.
As in, for round 1, it should be M6F5 vs M2F3, not M6F4 vs M7F7 as both M7 and F7 are in the other 2 matches for round 1. Otherwise, the rest of the table works out for 10 2/3 rounds.
Here's what I mean:

[Ian Wakeling]

Hi,  Thanks for letting me know about the error in the paper - I am sorry that you had to find out the hard way.  For the benefit of anyone else reading this, there is an example of the correct schedule here - see reply #6.  The paper itself can be found here.

I was looking at my computer search code again and I have managed to find a 9 round schedule that might be of some use:

(m01 f07 v m05 f06) (m02 f01 v m06 f02) (m08 f04 v m07 f08) (m03 f05 v m04 f03)
(m08 f06 v m04 f04) (m01 f03 v m03 f01) (m02 f02 v m05 f08) (m07 f07 v m06 f05)
(m07 f05 v m08 f08) (m04 f07 v m01 f02) (m05 f04 v m06 f03) (m02 f01 v m03 f06)
(m02 f06 v m07 f03) (m08 f01 v m05 f04) (m06 f07 v m01 f08) (m03 f02 v m04 f05)
(m02 f05 v m01 f04) (m05 f02 v m08 f06) (m07 f01 v m04 f07) (m03 f03 v m06 f08)
(m07 f04 v m03 f02) (m02 f07 v m04 f06) (m01 f01 v m08 f03) (m06 f08 v m05 f05)
(m07 f05 v m05 f01) (m01 f06 v m03 f08) (m04 f02 v m06 f04) (m08 f07 v m02 f03)
(m04 f08 v m05 f03) (m08 f02 v m03 f07) (m07 f06 v m06 f01) (m02 f04 v m01 f05)
(m01 f03 v m07 f02) (m02 f08 v m04 f01) (m08 f05 v m06 f06) (m03 f04 v m05 f07)

So above each player has
  1 repeated partner
  1 repeated opposite sex opponent
  2 repeated same sex opponents

Hope that helps.