Round Robin Tournament Scheduling

Schedules - You must register to Post and Download => Requests => Topic started by: morganc on February 19, 2008, 07:25:35 PM

Title: :Round Robin- 17 teams, 8 rooms (Battle of Books)
Post by: morganc on February 19, 2008, 07:25:35 PM
Hi Math Masterminds,

First of all, I really appreciate your forum.  You were a great resource to our school system last year. I have a background in math which is why I am asked to do the schedule for our county's Battle of Books competition for elementary and middle school kids.  

The competition will be 17 teams held in 8 classrooms.  And throw in a request to move them as little as possible.  I noticed that Julian Wiseman had posted a hit for a 17 team rotation on 5/3/07.  Will the same schedule work?  I had looked into creating my own using a hexadecagon, but it appeared to be a gargantuan task.

I am grateful for any assistance in this matter.
Chrissy  
Title: Re: :Round Robin- 17 teams, 8 rooms (Battle of Boo
Post by: wbport on February 19, 2008, 08:35:43 PM
This might be what you are looking for.  Ignore the first column (has the 18 in it), that team has a bye for that round. Except for the 1st, last, and round a team has a bye, they will spend two consecutive rounds in the same room.
17 or 18 players 
 1:    1-18  17-2   16-3   15-4   14-5   13-6   12-7   11-8   10-9 
 2:   18-10   2-1    3-17   4-16   5-15   6-14   7-13   8-12   9-11
 3:    2-18   1-3   17-4   16-5   15-6   14-7   13-8   12-9   11-10
 4:   18-11   3-2    4-1    5-17   6-16   7-15   8-14   9-13  10-12
 5:    3-18   2-4    1-5   17-6   16-7   15-8   14-9   13-10  12-11
 6:   18-12   4-3    5-2    6-1    7-17   8-16   9-15  10-14  11-13
 7:    4-18   3-5    2-6    1-7   17-8   16-9   15-10  14-11  13-12
 8:   18-13   5-4    6-3    7-2    8-1    9-17  10-16  11-15  12-14
 9:    5-18   4-6    3-7    2-8    1-9   17-10  16-11  15-12  14-13
10:   18-14   6-5    7-4    8-3    9-2   10-1   11-17  12-16  13-15
11:    6-18   5-7    4-8    3-9    2-10   1-11  17-12  16-13  15-14
12:   18-15   7-6    8-5    9-4   10-3   11-2   12-1   13-17  14-16
13:    7-18   6-8    5-9    4-10   3-11   2-12   1-13  17-14  16-15
14:   18-16   8-7    9-6   10-5   11-4   12-3   13-2   14-1   15-17
15:    8-18   7-9    6-10   5-11   4-12   3-13   2-14   1-15  17-16
16:   18-17   9-8   10-7   11-6   12-5   13-4   14-3   15-2   16-1 
17:    9-18   8-10   7-11   6-12   5-13   4-14   3-15   2-16   1-17
Title: Re: :Round Robin- 17 teams, 8 rooms (Battle of Boo
Post by: Ian Wakeling on February 21, 2008, 03:48:08 AM
Hi Chrissy,

wbport's schedule is really very nice indeed.  If you look at what happens at any of the 8 rooms in the gap between two rounds (again ignore the first column), one of the kids remains in the room, while the other kid either moves to another room or goes to have a bye.  So at every interval 8 kids remain where they are and 8 kids move out of the room.  It is easy to see that you can not do better than this, if 9 kids remained fixed, then at least 2 of them would have to be in the same room, and would oppose each other twice in a row, so the schedule could not be valid.  So the 8 kids fixed schedule must therefore be optimal.

Look closely at where the kids who move, move to.  If they don't get the bye then they always move to an adjacent room, so by assigning the columns carefully to the actual rooms you can minimise the travelling distance between rooms.  Also notice that the kid who gets the bye in round r,  returns in round (r+1) to the same room that they had in round (r-1), so it would reduce disruption further by telling the kid who gets the bye to wait outside the room they have just left.

If you do have 18 kids, then the schedule is still optimal as kid 18 never moves from room 1, so there are 9 rooms and 9 kids remain fixed between rounds.

It's amazing how wbport's schedule for chess tournaments has this alternative application.  If you look for his other postings and the links to the Java script generator then you will be able to make schedules for any number of kids.

I hope the competition goes well.

Ian.
Title: Re: :Round Robin- 17 teams, 8 rooms (Battle of Boo
Post by: wbport on February 21, 2008, 08:16:29 AM
Thank you for the plug.

My generator is here (http://home.comcast.net/~wporter211/realsite/chess_etc/rrpair.htm).  To create your table I chose "Porter" and "No Flop". The "Board Order" option shows the structure of a RR better while "Sequential Players" displays only the odd boards going out and the even boards coming back in. With No Flop, it alternates odd-even and even-odd so players won't appear to "flop" from one end of the table to the other.
Title: Re: :Round Robin- 17 teams, 8 rooms (Battle of Boo
Post by: wbport on April 17, 2008, 04:22:51 PM
The name of the No Flop option was changed to Min Moves on the link.