Thanks ... and question about round-robin

[Crystal(Guest)]

Thank you for this amazingly helpful service.  Is there a round-robin algorithm simulator that I could input different scenarios?  For instance, we are having a battle of the books competition and need the best simulation for 14 teams playing each other with a limit of 4 rooms with minimum movement (that's the problem).  Thank you!

[Ian Wakeling]

Crystal, please would you provide more details. How does the competition work? What do you mean by minimum movement?

Ian.

[Crystal(Guest)]

Here is the information that I was given:
14 teams, 4 rooms + holding area.  Each team must play all other 13 teams with as little movement as possible since the holding area is very small and to minimize congestion.  For instance, 4 teams could remain in the 4 rooms while the other teams rotated.  Only 4 rounds can take place at the same time.  The rest of the 6 teams will be waiting in the holding area.  The only thing that I could think of would be to have 4 teams remain in the rooms and take 4 more through a rotation.  For example, T1-T5, T2-T6, T3-T7, T4-T8... then rotate T5 through T8 for 3 more matches.  Then bring in T9-T12 for 4 rotations...and so forth.

Thank you so much for your input.

[Ian Wakeling]

This is a first, as I don't think anyone has asked before for the "minumum movement" property.  With 14 teams and 4 rooms you will need to have 23 rounds to go through the whole round-robin.  I don't really have any algorithms set up specifically to solve this sort of problem, but managed to put together the schedule below.

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

In particular there is a long run of C and I in room 2 (column 2) and runs of Bs and Ds in rooms 3 and 4 respectively.  I am fairly sure you can do a lot better than this (any other takers?).

Ian.

[Jeff]

Hi,
I took Ian's matrix and performed a convolution and found the following where every team plays in every room 3 times and one room 4 times.  No team plays in the same room twice in a row.

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

This should work for you as well.
Regards,
Jeff Bond