Round Robin Tournament Scheduling

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Title: 11 team round robin
Post by: suem on September 07, 2015, 08:44:38 PM

I recently asked about a 13 team round robin with some specific parameters and the answer I received worked perfectly.  Now I have the same scenario but with 11 teams that must play 3 matches per day for 2 days and then will play 2 matches on the third day. 3 courts can be used at one time.  If possible, teams can only play back to back time slots, once per day.  Each team does not need to play the same teams.  
 
So in the end, each team will play a minimum of 8 other teams.  But all teams must play the same number of matches over the 3 days.
 
I hope you can again help me.

Title: Re: 11 team round robin
Post by: Ian Wakeling on September 08, 2015, 04:21:27 AM

This is a harder problem than the 13 team one.  I believe I have a workable solution below, where again there is the odd empty slot in the schedule and again you will need to leave out the last four rounds.  The problem is that team D plays twice on day 1 and four times on day 2.  An alternative might be to have one extra empty slot on day 2, and remove the empty slot on day 3 - meaning 2 teams would play three times on day 3.

Schedule:

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

Team frequency in each round
     A B C D E F G H I J K
R001 1 0 0 0 0 0 1 1 1 1 1 
R002 0 1 1 1 1 0 0 0 0 0 0 
R003 1 0 0 0 0 1 0 1 1 1 1 
R004 0 1 1 0 1 0 1 0 0 0 0 
R005 1 0 0 1 0 1 0 1 0 1 1 
R006 0 1 1 0 1 1 1 0 1 0 0 
--------------------------
R007 0 0 0 1 1 1 1 1 0 1 0 
R008 1 1 1 0 0 0 0 1 1 0 1 
R009 0 0 0 1 1 1 1 0 0 0 0 
R010 1 1 1 0 0 0 0 0 1 1 1 
R011 1 0 0 1 1 1 1 1 0 0 0 
R012 0 1 1 1 0 0 0 0 1 1 1 
--------------------------
R013 1 1 0 1 0 1 0 0 1 1 0 
R014 0 0 0 0 1 0 1 1 0 0 1 
R015 1 1 1 1 0 1 0 0 1 0 0 
R016 0 0 1 0 1 0 1 1 0 1 1 
--------------------------
R017 0 1 1 1 0 0 0 1 1 1 0 
R018 1 0 1 0 1 1 1 0 0 0 1 
R019 0 0 0 1 0 0 0 1 1 1 0 
R020 1 1 0 0 1 1 1 0 0 0 1 

Title: Re: 11 team round robin
Post by: suem on September 08, 2015, 08:37:57 AM

Thank you again for your attention to this.  I, too, had already figured out where one team played twice on one day, but had to play 4 times on the second day.  So I thought I might be overlooking something.  I really appreciate your expertise in these problems.