Volleyball league

[deadlift]

I have the following situation this year in the Volleyball league:

3 divisions consisting of 12, 16, 16 teams respectively.

We run the league with 4 30 minute slots and I was planning on taking
half of the teams from each division so that would be 6, 8, 8 and
having them play in slot A and the other half playing in slot B.

The problem is that the same teams that played in slot A will have to
play in slot C and those from slot B will have to play in slot D.
Each team must play each other once.

So for example using the 12 team division:

A: 12 v 1, 11 v 2, 3 v 10

B: 9 v 4, 5 v 8, 7 v 6

C: 2 v 12, 1 v 3, 10 v 11

D: 6 v 9, 8 v 7, 4 v 5

and so on until everyone has played everyone once.  This used to work
when I had only two divisions but thus far I have failed to come up
with a schedule that does not fail as I get near the end.  Is there
some type of algorithm out there to generate this type of schedule
with a given number of teams either 12 or 16 in my case.

Thanks much

[Ian Wakeling]

If I understand correctly then I do have an algorithm that will attempt to solve this, but unfortunately it can't find perfect solutions.  For the 12 team division it gives:

(B J) (A G) (E K) 
(F L) (C H) (D I) 
(B L) (J K) (E G) 
(F H) (C D) (A I) 
------------------
(I K) (G H) (B D) 
(E J) (A F) (C L) 
(D H) (B K) (G I) 
(C E) (F J) (A L) 
------------------
(H K) (A B) (F I) 
(D E) (J L) (C G) 
(A K) (H I) (B F) 
(D G) (E L) (C J) 
------------------
(A C) (D L) (B H) 
(F K) (E I) (G J) 
(A D) (B C) (H L) 
(I J) (G K) (E F) 
------------------
(F G) (D J) (A H) 
(C I) (B E) (K L) 
(B G) (D F) (H J) 
(A E) (I L) (C K) 
------------------
(B I) (C F) (D K) 
(G L) (E H) (A J)

Above there are two times where a team has to play back-to-back matches.  L in week 1, and B in week 5.

For 16 teams it gives:

(L O) (I M) (F G) (B E) 
(C H) (A K) (N P) (D J) 
(B I) (E O) (D L) (G M) 
(F K) (J P) (A H) (C N) 
------------------------
(H I) (G N) (B J) (C O) 
(E L) (F P) (K M) (A D) 
(I N) (C J) (H O) (B G) 
(A M) (K L) (E P) (D F) 
------------------------
(D E) (C F) (B O) (M N) 
(A P) (I J) (H L) (G K) 
(E F) (C D) (B N) (M O) 
(A J) (G P) (H K) (I L) 
------------------------
(D P) (B H) (E I) (F M) 
(G J) (A O) (L N) (C K) 
(F H) (B D) (M P) (I O) 
(C G) (E K) (J N) (A L) 
------------------------
(E J) (F O) (D G) (H N) 
(B K) (L M) (A C) (I P) 
(G O) (H J) (F I) (E N) 
(C M) (A B) (D K) (L P) 
------------------------
(N O) (G I) (F L) (J K) 
(D M) (H P) (B C) (A E) 
(I K) (F N) (A G) (J L) 
(B M) (D O) (C P) (E H) 
------------------------
(A F) (B L) (E G) (C I) 
(O P) (K N) (J M) (D H) 
(G L) (C E) (A I) (B F) 
(D N) (H M) (J O) (K P) 
------------------------
(B P) (D I) (E M) (F J) 
(C L) (A N) (K O) (G H)

Here there 4 back-to-back matches.  D in week 1, O in week 4, I in week 5, and A in week 6.

Is that workable?

[deadlift]

Hi,
   Yes this is workable, but how did you do it?  I had that kind of overlap thing such as the "L" team thing happening every week.  Also to note that in week 1 team "A" has an hour gap instead of the usual 1/2 hour.  Since this only happens twice in the 5 1/2 weeks they can live with it I am curious as to how you came up with this assuming it can be explained in layman's terms.  In any event thank you very much - you have been a life saver how many sheets of paper and pencils have I used up!!!

Great site for all the suffering league directors out there

[Ian Wakeling]

I am using a computer algorithm that examines many different schedules and picks the best one, the schedules are not generated totally at random, rather it tries to find schedules similar to others that have good properties.

I have just left the 12 team problem running for a couple of hours and it has found a slightly better solution with only one inconsistency.

(E K) (I J) (A B) 
(G L) (D F) (C H) 
(B I) (J K) (A E) 
(F L) (D H) (C G) 
------------------
(D L) (E H) (G I) 
(C J) (A F) (B K) 
(D G) (E L) (H I) 
(B C) (A K) (F J) 
------------------
(G H) (F I) (C K) 
(A L) (B J) (D E) 
(F H) (C I) (K L) 
(E J) (B G) (A D) 
------------------
(I K) (A J) (H L) 
(C F) (E G) (B D) 
(A I) (H K) (J L) 
(B E) (C D) (F G) 
------------------
(D J) (I L) (B H) 
(A G) (C E) (F K) 
(H J) (B L) (D I) 
(A C) (G K) (E F) 
------------------
(B F) (A H) (E I) 
(D K) (C L) (G J)

Team L is back-to-back in week 3, while G gets the 1 hour break.

[deadlift]

And to think I was using pencil and paper - it would have taken me years if ever - what can I say....

Thanks again excellent work!!!!!